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Tamilnadu State Board New Syllabus Samacheer Kalvi 11th Maths Guide Pdf Chapter 12 Introduction to Probability Theory Ex 12.1 Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 12 Introduction to Probability Theory Ex 12.1

Question 1.
An experiment has the four possible mutually exclusive and exhaustive outcomes A, B, C, and D. Check whether the following assignments of probability are permissible.
(i) P (A) = 0.15, P (B) = 0.30,
P (C) = 0.43, P (D) = 0.12
Answer:
P(A) = 0.15, P(B) = 0.30, P(C) = 0.43, P(D) = 0.12
Now P(A) + P(B) + P(C) + P(D) = 0.15 + 0.30 + 0.43 + 0.12 = 1
0.15 + 0.30 + 0.43 + 0.12 = 1
∴ The assignment of probability is permissible.

(ii) P (A) = 0.22, P (B) = 0.38,
P (C) = 0.16, P (D) = 0.34
Answer:
Given that
P (A) = 0.22 ≥ 0,
P (B) = 0.38 ≥ 0,
P(C) = 0.16 ≥ 0 ,
P (D) = 0.34 ≥ 0
P(S) = P (A) + P(B) + P(C) + P(D)
= 0.22 + 0.38 + 0.16 + 0.34
= 1.1 > 1
Therefore the assignment of probability isn’t permissible

(iii) P(A) = \(\frac{2}{5}\), P(B) = \(\frac{3}{5}\),
P(C) = – \(\frac{1}{5}\), P(D) = \(\frac{1}{5}\)
Answer:
P(A) = \(\frac{2}{5}\), P(B) = \(\frac{3}{5}\), P(C) = \(-\frac{1}{5}\), P(D) = \(\frac{1}{5}\)
P(C) = \(-\frac{1}{5}\) which is not possible
(i.e.) for any event A, (0 ≤ P(A) ≤ 1)
∴ The assignment of probability is not permissible.

Question 2.
If two coins are tossed simultaneously, then find the probability of getting
(i) one head and one tail
(ii) at most two tails
Answer:
Two coins are tossed simultaneously = one coin is tossed two times.
The sample space S = { H , T } × { H , T }
S = {HH, HT, TH, TT }
n(S) = 4
Let A be the event of getting one head and one tail, B be the event of getting atmost two tails.
A = {HT, TH}
n(A) = 2
B = {HH, HT , TH, TT}
n (B) = 4

(i) P (getting one head and one tail)

(ii) P (getting atmost two tails)

Question 3.
Five mangoes and 4 apples are in a box. If two fruits are chosen at random, find the probability that
(i) one is a mango and the other is an apple
(ii) both are of the same variety.
Answer:
(i) One is a mango and the other is an apple:
Let S be the sample space, A be the event of taking one mango and one apple.
n(S) = 9C₂
n (A) = 5C₁ × 4C₁
= 5 × 4 = 20

(ii) Both are of the same variety:
Let S be the sample space, A be the event of taking 2 mangoes and B be the event of taking 2 apples
∴ n(s) = 9C₂

P(taking 2 fruits are of the same colour)
= P(A or B)
= P(A ∪ B)
= P(A) + P(B)

Question 4.
What is the chance that
(i) Non – leap year
Answer:
Non-leap year
No of days = 365
= \(\frac{365}{7}\) weeks = 52 weeks + 1 day
In 52 weeks we have 52 Sundays. So we have to find the probability of getting the remaining one day as Sunday. The remaining 1 day can be Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday
(i.e.,) n(S) = 7
In the n (Sunday) = A {Saturday to Sunday or Sunday to Monday}
(i.e.,) n(A) = 1
So, P(A) = 1.
∴ Probability of getting 53 Sundays \(\frac{n(\mathrm{A})}{n(\mathrm{S})}=\frac{1}{7}\)

(ii) Leap year should have fifty-three Sundays?
Answer:
In 52 weeks we have 52 Sundays. We have to find the probability of getting one Sunday to form the remaining 2 days can be a combination of the following S = {Saturday to Sunday, Sunday to Monday, Monday, to Tuesday, Tuesday to wednes¬day, Wednesday to Thursday, Thursday to Friday, Friday and Saturday}.
(i.e) n(s) =7
In this = A {Saturday to Sunday, Sunday to Monday}
(i.e) n(A) = 2
So, P(A) = \(\frac{2}{7}\)

Question 5.
Eight coins are tossed once, find the probability of getting
(i) exactly two tails
(ii) at least two tails
(iii) at most two tails
Answer:
Eight coins are tossed simultaneously one time = one coin is tossed eight times.
Let S be the sample space.
S = {H, T} × {H, T} × ………….. × {H, T} 8 times
Let A be the event of getting exactly two heads,
B be the event of getting atleast two tails and
C be the event of getting atmost two tails.
When eight coins are tossed, the number of elements in the sample space
n(S) = 2⁸ = 256
n(A) = 8C₂
= \(\frac{8 \times 7}{1 \times 2}\) = 28
n (B) = 8C₂ + 8C₃ + 8C₄ + 8C₅ + 8C₆ + 8C₇ + 8C₈
= n (S) – (8C₈ + 8C₁)
= n (S) – {n (Event of getting all heads) + n (Event of getting one head)}
= n(S) – (1 + 8)
= 256 – 9 = 247
n (C) = 8C₀ + 8 C₁ + 8 C₂
= 1 + 8 + \(\frac{8 \times 7}{1 \times 2}\)
= 1 + 8 + 28 = 37

(i) P {getting exactly two tails) =

(ii) P (getting atleast two tails ) =

(iii) P (getting atmost two tails) =

Question 6.
An integer is chosen at random from the first 100 positive integers. What is the probability that the integer chosen is a prime or multiple of 8 ?
Answer:
Let S be the sample space
S = { 1, 2, 3, …………., 100 }
Let A be the event of choosing a prime number
A = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}
n(A) = 25
Let B be the event of choosing an integer a multiple of 8.
B = { 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
n(B) = 12
P(Choosing a prime number) = P(A)

P (Choosing an integer a multiple of 8) = P (B)

P ( Choosing an integer a prime or multiple of 8)
= P(A or B)
= P(A ∪ B)
P(A) + P(B)
(since A and B are mutually exclusive that is A ∩ B = Φ)

Question 7.
A bag contains 7 red 4 black balls, 3 balls are drawn at random. Find the probability that
(i) all are red
(ii) one red and 2 black.
Answer:
Let S be the sample space, A be the event of taking 3 red balls and B be the event of taking one red and
2 black balls.
A bag contains 7 red balls and 3 black balls.
3 balls are drawn at random.
∴ The number of outcomes n(S) = 11C₃
= \(\frac{11 \times 10 \times 9}{1 \times 2 \times 3}\)
= 11 × 5 × 3 = 165

n (A) = 7C₃

n(B) = 7C₁ × 4C₂
= 7 × \(\frac{4 \times 3}{1 \times 2}\) = 7 × 6 = 42

(i) p (getting 3 red balls) = p(A)

(ii) p (getting one red and 2 blacks) = p(B)

Question 8.
A single card is drawn from a pack of 52 cards. What is the probability that
(i) the card is an ace or a king
(ii) the card w11 be 6 or smaller
(iii) the card is either a queen or 9?
Answer:
S be the sample space one card is drawn from a pack of 52 cards.
∴ n(S) = 52C₁
n(S) = 52

(i) The card is an ace or a king
Let A be the event of getting an ace.
n(A) = 4C₁ = 4
Let B be the event of getting a king.
n(B) = 4C₁ = 4
P (getting an ace or a king)
= P(A or B)
= P(A ∪ B)
= P(A) + P(B)
(since A and B are mutually exclusive events, A ∩ B = Φ)

(ii) The card will be 6 or smaller:
Let A be the event of getting a number 6.
∴ n(A) = 4C₁ = 4
Let B be the event of getting numbers less than 6.
n(B) = 16C₁ = 16
P (the card will be 6 or less than 6)
= P(A or B)
= P(A ∪ B)
= P(A) + P(B)
(since A and B are mutually exclusive events A ∩ B = Φ)

(iii) The card is either a queen or 9?
Let A be the event of getting a Queen.
∴ n(A) = 4C₁ = 4
Let B be the event of getting a number 9.
n(B) = 4C₁ = 4
P (the card is either a Queen or 9)
= P(A or B)
= P(A ∪ B
= P(A) + P(B)
(since A and B are mutually exclusive events)

Question 9.
A cricket club has 16 members, of whom only 5 can bowl. What is the probability that in a team of 11 members at least 3 bowlers are selected?
Answer:
Number of members in the cricket club = 16
Number of bowlers = 5
Number of batters = 16 – 5 = 11
The probability that a team of 11 members consisting of atleast 3 bowlers = (Probability of selecting 3 bowlers and 8 batters) + ( Probability of selecting 4 bowlers and 7 batters) + (Probability of selecting 5 bowlers and 6 batters)
The probability that a team of 11 members consisting of atleast 3 bowlers

[Selection procedure:
First out of total 16 members selecting 11 members in 16C₁₁ ways.
Selection of 11 members consisting minimum of 3 bowlers.
∴ Selection of 11 members as follows
(1) 3 bowlers from 5 bowlers and 8 batters from 11 batters.
(2) 4 bowlers from 5 bowlers and 7 batters from 11 batters.
(3) 5 bowlers from 5 bowlers and 6 batters from 11 batters.]

Question 10.
(i) The odds that event A occurs is 5 to 7, find P(A).
Answer:
Given the odds, that event A occurs is 5 to 7.

(ii) Suppose p (B) = \(\frac{2}{5}\). Express the odds that the event B occurs.
Answer:

∴ The odds that the event B occurs is 2 to 3.

Tamilnadu State Board New Syllabus Samacheer Kalvi 11th Maths Guide Pdf Chapter 11 Integral Calculus Ex 11.13 Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.13

Choose the correct or the most suitable answer from given four alternatives.

Question 1.
If ∫ f(x) dx = g(x) + c. then ∫ f(x) g (x)dx
(1) ∫ (f(x)² dx
(2) ∫ f(x) g(x) dx
(3) ∫ f'(x) g(x) dx
(4) ∫ (g(x))² dx
Answer:
(1) ∫ (f(x)² dx

Explaination:
Given ∫ f (x) dx = g (x) + c
\(\frac{\mathrm{d}}{\mathrm{d} x}\) ∫ f(x)dx = \(\frac{\mathrm{d}}{\mathrm{d} x}\) (g(x) + c)
∫ \(\frac{\mathrm{d}}{\mathrm{d} x}\) (f(x)) dx = g'(x)
∫ d(f(x)) = g'(x)
f(x) = g(x)
∴ ∫ f(x) g'(x) dx = ∫ f(x) f(x) dx
= ∫ [f(x)]² dx

Question 2.
If \(\int \frac{3^{\frac{1}{x}}}{x^{2}}\) dx = k\(\left(3^{\frac{1}{x}}\right)\) + c, then the value of k is
(1) log 3
(2) – log 3
(3) \(-\frac{1}{\log 3}\)
(4) \(\frac{1}{\log 3}\)
Answer:
(3) \(-\frac{1}{\log 3}\)

Explaination:

Question 3.
If ∫ f'(x) e^x2 dx = (x – 1)e^x2 + c, then f(x) is
(1) 2x³ – \(\frac{x^{2}}{2}\) + x + c
(2) \(\frac{x^{3}}{2}\) + 3x² + 4x + c
(3) x³ + 4x² + 6x + c
(4) \(\frac{2 x^{3}}{3}\) – x² + x + c
Answer:
(4) \(\frac{2 x^{3}}{3}\) – x² + x + c

Explaination:
Given ∫ f'(x) e^x2 dx = (x – 1)e^x2 + c
Differentiating both sides with respect to x we have

Question 4.
The gradient (slope) of a curve at any point (x, y) is \(\frac{x^{2}-4}{x^{2}}\). If the curve passes through the point (2, 7), then the equation of the curve is
(1) y = x + \(\frac{4}{x}\) + 3
(2) y = x + \(\frac{4}{x}\) + 4
(3)y = x² + 3x + 4
(4) y = x² – 3x + 6
Answer:
(1) y = x + \(\frac{4}{x}\) + 3

Explaination:


Given, this curve passes through the point (2, 7)
∴ 7 = 2 + \(\frac{4}{2}\) + c
7 = 2 + 2 + c
c = 7 – 4 = 3
∴ The required equation is
y = x + \(\frac{4}{x}\) + 3

Question 5.

(1) cot (xe^x) + c
(2) sec (xe^x) + c
(3) tan (xe^x) + c
(4) cos (xe^x) + c
Answer:
(3) tan (xe^x) + c

Explaination:

= ∫sec² t
= tan t + c
= tan (x e^x) + c

Question 6.

(1) \(\sqrt{\tan x}+\mathbf{c}\)
(2) \(2 \sqrt{\tan x}+\mathbf{c}\)
(3) \(\frac{1}{2} \sqrt{\tan x}+c\)
(4) \(\frac{1}{4} \sqrt{\tan x}+c\)
Answer:
(1) \(\sqrt{\tan x}+\mathbf{c}\)

Explaination:

Question 7.
∫sin³ dx is
(1)
(2)
(3)
(4)
Answer:
(3)

Explaination:
∫sin³ dx
sin 3x = 3 sin x – 4 sin³ x
4 sin³ x = 3 sin x – sin 3x
sin³ x = \(\frac{1}{4}\)(3 sin x – sin 3x)

Question 8.

(1) x + c
(2) \(\frac{x^{3}}{3}\) + c
(3) \(\frac{3}{x^{3}}\) + c
(4) \(\frac{1}{x^{2}}\) + c
Answer:
(2) \(\frac{x^{3}}{3}\) + c

Explaination:

Question 9.

(1) tan^-1 (sin x) + c
(2) 2 sin^-1 (tan x) + c
(3) tan^-1 (cos x) + c
(4) sin^-1 (tan x) + c
Answer:
(4) sin^-1 (tan x) + c

Explaination:

Question 10.

(1) x² + c
(2) 2x² + c
(3) \(\frac{x^{2}}{2}\) + c
(4) – \(\frac{x^{2}}{2}\) + c
Answer:
(3) \(\frac{x^{2}}{2}\) + c

Explaination:

Question 11.
∫2^3x+5 dx is
(1)
(2)
(3)
(4)
Answer:
(4)

Explaination:
∫2^3x+5 dx
Put 3x + 5 = t
3 dx = dt
dx = \(\frac{1}{3}\) dt

Question 12.

(1) \(\frac{1}{2}\) sin 2x + c
(2) –\(\frac{1}{2}\) sin 2x + c
(3) \(\frac{1}{2}\) cos 2x + c
(4) –\(\frac{1}{2}\) cos 2x + c
Answer:
(2) –\(\frac{1}{2}\) sin 2x + c

Explaination:

Question 13.

(1) e^x tan^-1 (x + 1) + c
(2) tan^-1 (e^x) + c
(3) e^x \(\frac{\left(\tan ^{-1} x\right)^{2}}{2}\) + c
(4) e^x tan^-1 x + c
Answer:
(4) e^x tan^-1 x + c

Explaination:

Question 14.

(1) cot x + sin^-1 x + c
(2) – cot x + tan^-1x + c
(3) – tan x + cot^-1 x + c
(4) – cot x – tan^-1x + c
Answer:
(4) – cot x – tan^-1x + c

Explaination:

Question 15.
∫x² cos x dx is
(1) x² sin x + 2x cos x – 2 sin x + c
(2) x² sin x – 2x cos x – 2 sin x + c
(3) – x² sin x + 2x cos x + 2 sin x + c
(4) – x² sin x – 2x cos x + 2 sin x + c
Answer:
(1) x² sin x + 2x cos x – 2 sin x + c

Explaination:
\(\int x^{2} \cos x d x\)
By Bernoullis formula dv = cosxdx
u = x² v = sinx
u’ = 2x v₁ = -cos x
u” = 2 v₂ = -sinx
= uv – u’v₁ + u”v₂
= x²sin x + 2x cos x – 2 sin x + c

Question 16.

(1)
(2)
(3)
(4)
Answer:
(1)

Explaination:

Question 17.
\(\int \frac{d x}{e^{x}-1}\) is
(1) log |e^x| – log |e^x – 1| + c
(2) log |e^x| + log |e^x – 1| + c
(3) log |e^x – 1| – log |e^x| + c
(4) log |e^x + 1| – log |e^x| + c
Answer:
(3) log |e^x – 1| – log |e^x| + c

Explaination:

Question 18.
∫e^-4x cos x dx is
(1) \(\frac{e^{-4 x}}{17}\) [4 cos x – sin x] + c
(2) \(\frac{e^{-4 x}}{17}\) [- 4 cos x – sin x] + c
(3) \(\frac{e^{-4 x}}{17}\) [4 cos x + sin x] + c
(4) \(\frac{e^{-4 x}}{17}\) [- 4 cos x – sin x] + c
Answer:
(2) \(\frac{e^{-4 x}}{17}\) [- 4 cos x – sin x] + c

Explaination:

Question 19.

(1)
(2)
(3)
(4)
Answer:
(4)

Explaination:

Question 20.
∫e^-7x sin 5x dx is
(1) \(\frac{e^{-7 x}}{74}\) [- 7 sin 5x – 5 cos 5x] + c
(2) \(\frac{e^{-7 x}}{74}\) [7 sin 5x + 5 cos 5x] + c
(3) \(\frac{e^{-7 x}}{74}\) [7 sin 5x – 5 cos 5x] + c
(4) \(\frac{e^{-7 x}}{74}\) [- 7 sin 5x + 5 cos 5x] + c
Answer:
(1) \(\frac{e^{-7 x}}{74}\) [- 7 sin 5x – 5 cos 5x] + c

Explaination:

Question 21.
∫x² e^x/2 dx is
(1)
(2)
(3)
(4)
Answer:
(3)

Explaination:

Question 22.

(1)
(2)
(3)
(4)
Answer:
(4)

Explaination:

Question 23.

(1)
(2)
(3)
(4)
Answer:
(3)

Explaination:

Question 24.
∫sin √x dx is
(1) 2(- √x cos √x + sin √x) + c
(2) 2(- √x cos √x + sin √x) + c
(3) 2(- √x sin √x – cos √x) + c
(4) 2(- √x sin √x + cos √x) + c
Answer:
(1) 2(- √x cos √x + sin √x) + c

Explaination:

Question 25.

(1)
(2)
(3)
(4)
Answer:
(4)

Explaination:

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Accountancy Guide Pdf Chapter 4 Goodwill in Partnership Accounts Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Accountancy Solutions Chapter 4 Goodwill in Partnership Accounts

12th Accountancy Guide Goodwill in Partnership Accounts Text Book Back Questions and Answers

I Multiple Choice Questions

Choose the correct answer

Question 1.
Which of the following statement is true?
(a) Goodwill is an intangible asset
(b) Goodwill is a current asset
(c) Goodwill is a fictitious asset
(d) Goodwill cannot be acquired
Answer:
(a) Goodwill is an intangible asset

Question 2.
Super profit is the difference between
(a) Capital employed and average profit
(b) Assets and liabilities
(c) Average profit and normal profit
(d) Current year’s profit and average profit
Answer:
(c) Average profit and normal profit

Question 3.
The average rate of return of similar concerns is considered as
(a) Average profit
(b) Normal rate of return
(c) Expected rate of return
(d) None of these
Answer:
(b) Normal rate of return

Question 4.
Which of the following is true?
(a) Super profit = Total profit / number of years
(b) Super profit = Weighted profit / number of years .
(c) Super profit = Average profit – Normal profit
(d) Super profit = Average profit × Years of purchase
Answer:
(c) Super profit = Average profit – Normal profit

Question 5.
Identify the incorrecte pair
(a) Good will under average profit method – Average profit × Number of years of purchase
(b) Goodwill under Super profit method – Super profit × Number of years of purchase
(c) Goodwill under Annuity method – Average Profit × Present value annuity factor
(d) Goodwill under Weighted average profit method – Weighted average profit x Number of years of purchase
Answer:
(c) Goodwill under Annuity method – Average Profit x Present value annuity factor

Question 6.
When the average profit is ₹ 25,000 and the normal profit ₹ 15,000 super profit is
(a) ₹ 25,000
(b) ₹ 5,000
(c) ₹ 10,000
(d) ₹ 15,000

Hints: Find out Super Profit
Super Profit = Average Profit – Normal Profit
= 25,000- 15,000
= ₹ 10,000
Answer:
(c) ₹ 10,000

Question 7.
Book profit of 2017 is ₹ 35,000; non -recurring income included in the profit is ₹ 1,000 and abnormal loss charged in the year 2017 was ₹ 2,000, then the adjusted profit is
(a) ₹ 36,000
(b) ₹ 35,000
(c) ₹ 38,000
(d) ₹ 34,000
Hints:

Answer:
(a) ₹ 36,000

Question 8.
The total capitalised value of a business is ₹ 1,00,000; asset are ₹ 1,50,000 and liabilities ₹ 80,000. the value of goodwill as per the capitalisation method will be
(a) ₹ 40,000
(b) ₹ 70,000
(c) ₹ 1,00,000
(d) ₹ 30,000
Hints:
Goodwill = Total capitalized value of the business – Actual capital employed
i) Capital employed = Fixed Assets + Current assets – Current Liabilities
= 1,50,000-80,000
= ₹ 70,000
ii) Capitalized Value = ₹ 1,00,000
= 1,00,000 – 70,000
= ₹ 30,000
Answer:
(d) ₹ 30,000

II. Very Short Answer Questions

Question 1.
What is goodwill?
Answer:
Goodwill is the good name or reputation of the business which brings benefit to the business. It enables the business to earn more profit. It is the present value of a firm’s future excess earnings.

Question 2.
What has acquired goodwill?
Answer:
Goodwill acquired by making payment in cash or kind is called acquired or purchased goodwill. When a firm purchases an existing business, the price paid of the purchase of such a business may exceed the net assets (Assets – Liabilities) of the business acquired. The excess of purchase consideration over the value of net assets acquired is treated as acquired goodwill.

Question 3.
What is super profit?
Answer:
Super profit is the excess of average profit over the normal profit of a business.
Super Profit = Average Profit – Normal Profit

Question 4.
What is normal rate of return?
Answer
:It is the rate at which profit is earned by similar business entities in the industry under normal circumstances.

Question 5.
State any two circumstances under which goodwill of a partnership firm is valued
Answer:

1. When there is a change in the profit-sharing ratio
2. When a new partner is admitted into a firm
3. When an existing partner retires from the firm or when a partner dies.
4. When a partnership firm is dissolved.

III Short Answer Questions

Question 1.
State any six-factor determining goodwill.
Answer:

1. Profitability of the firm.
2. Favourable location of the business enterprise.
3. Good quality of goods or services offered.
4. Tenure of the business enterprise.
5. Efficiency of management.
6. Degree of competition.
7. Other factors.

Question 2.
How is goodwill calculated under the super profits method?
Answer:
Under these methods, super profit is the base for calculation of the value of goodwill. Super profit is the excess of average profit over the normal profit of a business.
Super profit = Average profit – Normal profit

Average profit is calculated by dividing the total of adjusted actual profits of certain number of year by the total number of such years. Normal profit is the profit earned by the similar business firms under normal conditions.
Normal profit = Capital employed × Normal rate of return
Capital employed = Fixed assets + Currents assets – Current liabilities.

Question 3.
How is the value of goodwill calculated under the capitalisation method?
Answer:
Under these methods, super profit is the base for calculation of the value of goodwill. Super profit is the excess of average profit over the normal profit of a business.
Goodwill = Total capitalised value of the business – Actual capital employed
The total capitalised value of the business is calculation by capitalising the average profit on the basis of the normal rate of return.
Capitalised value of the business = \(\frac{\text { Average profit }}{\text { Normal rate of return }} \times 100\)
Actual capital employed = Fixed assets (excluding goodwill) + Current assets – Current liabilities

Question 4.
Computer average profit from the following information.
2016: ₹ 8,000; 2017: ₹ 10,000; 2018: ₹ 9,000
Solution:

Question 5.
Calculate the value of goodwill at 2 Years purchase of average profit when average profit is? 15,000.
Solution:
Goodwill = Average profit x No. of years of purchase
Goodwill = 15,000 x 2 Years
= Rs. 30,000

IV Exercises

Simple average profit method

Question 1.
The following are the profits of a firm in the last five years:
2014 : ₹ 10,000; 2015 : ₹ 11,000;
2016 :  ₹ 12,000; 2017 : ₹ 13,000; and 2018 : ₹ 14,000
Calculate the value of goodwill at 2 years purchase of average profit of five years.
Solution:
G/W = Average profit x No.of years of purchase

Answer :
Average profit: ₹ 12,000, Goodwill: ₹ 24,000

Question 2.
From, following information, calculate the value of goodwillOn the basis of 3 years purchase of average profits of last four years.

Solution:
G/W = Average profit x No.of years of purchase

Gs/W = 4,000 × 3 years = Rs. 12,000
Answer:
Average profit: ₹ 4,000; Goodwill: ₹ 12,000

Question 3.
From the following information relating to a partnership firm, find out the value of its goodwill based on 3 years purchas of average profits of the last 4 years.
(a) Profit of the years 2015, 2016, 2017 and 2018 are ₹ 10,000, ₹ 12,500, ₹ 12,000 and ₹ 11,500 respectively.
(b) The business was looked after by a partner and his fair remuneration amounts to ₹ 1,500, per year. This amount was not considered in the calculation of the above profits.
Solution:
G/W = Average profit = Average profit x No.of years of purchase

G/W Average profit × No.of years of purchase
= 10,000 × 3yrs
G/W = Rs. 30,000
Answer:
Average profit: ₹ 10,000; Goodwill: ₹ 30,000

Question 4.
From the following information relating to Sridevi enterprises, cal te the value of goodwill on the basis of 4 years pruchase of the average profits of 3 years.
(a) Profits for the years ending 31st December 2016, 2017 and 2018 were ₹ 1,75,000, ₹ 1,50,0 and ₹ 2,00,000 respectively.
(b) A non-recurring-income of ₹ 45,000 is include in the profits of the year 2016.
(c) The closing stock of the year 2017 was overvalued by ₹ 30,000.
Solution:
Calculation of Adjusted profit

Note : Overvaluationof cl. Stock in 2017 will results in over valuation of opening stock in 2018
Average Profit.
Average Profit. = \(\frac{1,30,000+1,20,000+2,30,00}{3}\)
Average Profit = \(\frac{4,80,000}{3}\)
= Rs. 1,60,000
= Average profit x No.of years of purchase
= 1,60,000 x 4 yrs
= Rs. 6,40,000
Answer :
Average profit: ₹ 1,60,000; Goodwill: ₹ 6,40,000

Question 5.
The following particulars are available in respect of the business carried on by a partnership firm:
(i) Profit earned : 2016 ₹ 25,000; 2017: ₹ 23,000 and 2018: ₹26,000.
(ii) Profit of 2016 includes a non-recurring income of ₹ 2,500.
(iii) Profit of 2017 is reduced by ₹ 3,500 due to stock destroyed by fire.
(iv) The stock was not insured. But, it is decided to insure the stock in future. The insurance premium is estimated to be ₹ 250 per annum.
you are required to calculate the value of goodwill of the firm on the basis of 2 years purchase of average profits of the last three years.
Solution:
Calculation of Adjusted profit

G/W = Average profit × No.of years of purchase
G/W = 24,750 × 2 yrs
= Rs. 49,500
Answer:
Average profit: ₹ 24,750; Goodwill: ₹ 49,500

Weighted average profit method.

Question 6.
Find out the value of goodwill at three years pruchase of weighted average profit of last four years.

Solution:
Calculation of Weighted Average profit

Weighted profts = \(\frac{\text { Weighted profts }}{\text { Total of weights }}\)
Av.pft = \(\frac{1,54,000}{10}\) = Rs. 15,400
G/w = Weighted Average profit × No. of yrs of purchase
G/w = 15,400 × 3yrs
= Rs. 46,200
Answer:
Average profit: ₹15,400; Goodwill: ₹ 46,200

Purchase of super profit method

Question 7.
From the following details, calculate the value o oodwill at 2 years purchase of super profit:
(a) Total assets of a firm are ₹ 5,00,000;
(b) The liabilities of the firm are ₹ 2,00,000
(c) Normal rate of return in this class of business is 12.5%.
(d) Average profit of the firm is ₹ 60,000.
Solution:
G/W = Super Profit x No.of years of purchase

Cap. Emp = Total Assets – Total liabilities
= 5,00,000 – 2,00,000
= Rs. 3,00,000
Normal Profit = \(\frac{3,00,000 \times 12.5}{100}\)
Rs. 37,500
Average Profit = Rs. 60,00
Super profit = Average Profit – Normal profit
= 60,000 – 37,500
= Rs. 22,500
G/w = 22,500 x 2 yrs
= Rs. 45,000
Answer:
Super profit: ₹ 22,500; Goodwill: ₹ 45,000

Question 8.
A partnership firm earned net profits during the last three years as follows:
2016 ₹ 20,000; 2017: ₹ 17,000 and 2018: ₹ 23,000.
The capital investement of the firm throghout the above mentioned period has been ₹ 80,000. Having regard to the risk involved, 15% is considered to the a fair return on capital employed in the business. Calculate the value of goodwill on the basis of 2 years purchase of super profit.
Solution:
G/W = Super Profit x No.of years of purchase

Super profit = Average Profit – Normal profit
= 20,000 – 12,000
= Rs. 8,000
G/w = 8,000 x 2 yrs
= Rs. 16, 000
Answer :
Super profit: ₹ 8,000; Goodwill: ₹ 16,000

Annuity Method:

Question 9.
From the following information, calculate the value of goodwill under annuity method:

Present value of ₹ 1 for 5 years at 15% per annum as per the annuity table is 3.352
Solution:
G/W = Super Profit x Value of A nnuity
SuPer profit = Average Profit – Normal Profit
SuPer profit = 14,000- 4,000 = Rs. 10,000
G/w = 10.0 x 3.352 = Rs. 33,520
Answer :
Super profit: ₹ 10,000; Goodwill: ₹ 33,520

Capitalisation of super profit method:

Question 10.
Find out the value of goodwill by caitalising super profits:
(a) Normal Rate of Return 10%
(b) Profits for the last four years are ₹ 30,000, ₹ 40,000, ₹ 50,000, ₹ 45,000,
(c) A non-recurring income of ₹ 3,000 is included in the above mentioned profit of ₹ 30,000,
(d) Average capital employed is ₹ 3,00,000.
Solution:

= Rs. 30,000
Super profit – Average Profit – Normal Profit
Super Profit – 40,500 – 30,000
= Rs. 10,500

Answer :
Super Profit: ₹ 10,500; Good will: ₹ 1,05,000

Question 11.
From the following information, find out the value of goodwill by capitalisatio method:
(i) Average profit ₹ 20,000
(ii) Normal rate of return 10%
(iii) Tangible assets of the firm ₹ 2,20,000
(iv) Liabilities of the firm ₹ 70,000.
Solution:
G/W = Total capitalaised Value of the business – Actual cap.Employee Average Profit

Actual cap employed = Tangible Assets – Liabilities of the firm.
= 2,20,000 – 70,000
= Rs. 1,50,000
G/w = 2,00,000 – 1,50,000
= Rs. 50,000
Answer:
Total Capitalised value: ₹ 2,00,000; Net tangible assets: ₹ 1,50,000; Goodwill: ₹ 50,000

12th Accountancy Guide Goodwill in Partnership Accounts Additional Important Questions and Answers

Question 1.
The excess of average profit over normal profit is
(a) Super profit
(b) Goodwill
(c) Undistributed profit
Answer:
(a) Super profit

Question 2.
The goodwill that can be recoreded in the books of accounts and is shown on the assets side of the B/S is
(a) Acquired goodwill
(b) Self-Generated goodwil
(c) None of these two
Answer:
(a) Acquired goodwill

Question 3.
How many methods are there for valuing G/W?
(a) 3
(b) 2
(c) 5
Answer:
(a) 3

III Short Answer Questions

Question 4.
Describe the nature of G/W.
Answer:
The nature of goodwill can be described as follows:

• Goodwill is an intangible fixed asset. It is intangible because it has no physical existence. It cannot be seen or touched.
• It has a definite value depending on the profitability of the business enterprise.
• It cannot be separated from the business.
• It help in earning more profit and attracts more customers.
• It can be purchased or sold only when the business is purchased or sold in full or in part.

Question 5.
Explain any 5 factors that determine the value of G/W
Answer:
Factors determining the value of goodwill of a partnership firm
(i) Profitability of the firm
The profit earning capacity of the firm determines the value of its goodwill. A firm earning higher profits and having potential to generate higher profits in future will have higher value of goodwill.

(ii) Favourable location of the business enterprise
If the firm is located in a prominent place which is easily accessible to the customers, it can attract more customers. Its sales and profit will be higher when compared to a firm which is not located in a prominent place. Hence, it will ahve high value of goodwill.

(iii) Good equality of goods or services offered
If a firm is located in a prominent place which is easily accessible to the customers, it can attract more customers. Its sales and profit will be higher when compared to a firm which is not located in a prominent place. Hence, it will have high value of goodwill.

(iv) Tenure of the business enterprise
A firm which has caried on business for several years will have higher reputation among its customers as it is better known to the customers. Such a firm will have higher earnings and higher value of goodwill when compared to a new firm.

(v) Efficiency of management
A firm having efficient management will earn more profitsa and the value of its goodwill will be higher compared to a firm with less efficient managerial personnel.
(iii) It cannot be separated from the business.

Question 6.
What do you mean by self generated G/W?
Answer:
It is the goodwill which is self generated by a firm based on features of the business such as favourable location, loya customers, etc. Such self-generated goodwill cannot be recorded in the books of accounts.

Question 7.
How do you calculated Adjusted Profit?
Answer:
Adjusted profit = Actual profit
+ Past expanse not required in the future.
– Past revenues not likely to be earned in the future
+ Additional income expected in the future
– Additional expenses expected to be paid in the future

Question 8.
How do you calculate G/W under weighted average profit method?
Answer:
Weighted average profit method
Under this method, goodwill is calculated by mulitplying the weighted average profit by a certain number of years of purchase.
Goodwill = Weighted average profit × Number of years of purchase

In this method, weights are assigned to each year’s profit. Weighted profit is ascertained by multiplying the weights assigned with the respective years profit. The sum of the wieghted profits is divided by the sum of weights assigned to determine the weighted averagge profit.

Weighted average profit = \(\frac{\text { Total of weighted profits }}{\text { Total of weights }}\)

Question 9.
What do you mean by Annuity Method of valuing G/w?
Answer:
Under this method, value of goodwill is calculated by multiplying the super profit with the present value of annuity.
Goodwill = Super profit x Present value annuity factor
Present value annuity factor is the present value of annuity of rupee one at a given time. It can be found out from annuity table or by using formula.
Annuity factor = \(\frac{\mathrm{i}(1+\mathrm{i})^{\mathrm{n}}}{\mathrm{i}(1+\mathrm{i})^{\mathrm{n}-1}}\)
Where i = interest rate
n = estimated number of years.

Question 10.
Write the formula for calcultaing G/w under capitalisation of Super profit method.
Answer:

IV Additional Problems:

Question 1.
The Goodwill is to be valued at two years purchase of last four years average profit. The profit were Rs. 40,000, Rs. 32,000, Rs. 15,000 and Rs. 13,000 respectively. Find out the value of goodwill.
Solution :
a) Calculation of average profit:

Calculation of Goodwill:
Goodwill = Average Profit × two years purchase
= 25,000 × 2
= Rs. 50,000.

Question 2.
Three year’s purchase of the last four years average profits is eed the value of goodwill. The profits and losses for the last four years are: I year Rs. 50,000, II year Rs. 80,000; III year Rs. 30,000 (Loss): IV year Rs. 60,000.
Calculate the amount of goodwill.
Solution:
a) Calculation of average Profit:

Total profit No. of years 1,60,000

Calculation of Goodwill:
Goodwill = Average Profit × three year’s purchase
= 40,000 × 3
= Rs. 1,20,000

Question 3.
A finis’:-‘ net profits durL the last three years were Rs. 90,000, Rs. 1,00,000 and Rs. 1,10,000. The capital employed in the firm is Rs. 3,00,000. A normal return on the capital is 10%. Calculate the value of goodwill on the basis of two year’s pruchase of super p it.
Solution:
a) Calculation of average Profit:

Calculation of Super Profit:
Sceper Profit = Average Profit – Normal Profit
= 1,00,000 – 30,000
= Rs. 70,000

Goodwill at two years purchase of super profit:
Goodwill = Super Profit × No. of years of purchase
= 70,000 × 2
= Rs. 1,40,000

Question 4.
Goodwill is to be valued at three years purchase of five year’s average profits. The profits – for the last five years of the firm were: 2,000-Rs.4,200; 2001-Rs.4,500; 2002-Rs.4,700; 2003-Rs.4,600; and 2004-Rs.5,000.
Solution
G/W = Average Profits x No. of yrs of purchase
Average Profit = \(\frac{4200+4500+4700+4600+5000}{5}\)
Average Profit = \(\frac{23,000}{5}\)
= Rs. 4,600
G/W = 4,600 × 3yrs
= Rs. 13,800

Question 5.
Calculate the amount of goodwill on the basis of two year’s purchase of the last four years average profits. The profits for the last four year’s are:

Solution:
Average Profit = \(\frac{26,000+34,000+50,000-10,000}{4}\)
Average Profit = 25,000
G/W = Average Profits × No. of yrs of purchase
G/W = 25,000 × 2
= Rs. 50,000

Question 6.
A firm earned net profits during the last three years as follows:

The Capital inverstment of the firm is Rs. 1,20,000. A fair return on the capital having regard to the risk involved in 10% calculate the value of goodwill on the basis of three years purchase of super profits.
Solution:

1,20,000 x \(\frac{10}{100}\) = Rs. 12,000
Super Profit = Average profit – Normal profit
= 40,000 – 12,000
Rs. 28,000
G/w = Super profit × No. of. yrs of purchase
= 28,000 × 3 years.
G/w = Rs. 84,000

Question 7.
From the following information, calculate the value of goodwill at three year’s purchase of super profit.
Average Capital employed in the business Rs. 6,00,000
Net trading profits of the firm for the past three years were Rs. .1,07,600, Rs. 90,700 and Rs. 1,12,500.
Rate of interest expected from capital having to the risk involved is 12%.
Fair remuneration to the partners for their service Rs. 12,000 p.a.
Solution:
Average Profit = \(\frac{1,07,600+90,700+1,12,500}{3}\)
Average Profit = \(\frac{3,10,800}{3}\)= Rs. 1,03,600
Profit before adj of renumeration = Rs. 1,03,600
Less Remineration = 12,000
Avg. Profit = 91,600
Normal Profit = \(\frac{\text { Cap. Emp } \times \text { Normal rate }}{100}\)
= \(6,00,000 \times \frac{12}{100}\)
= Rs. 72,000

Super Profit = Average Profit – Normal Profit
= 91,600 – 72,000
= Rs. 19,600

G/w = Super profit x No. of yrs of purchase
= 19,600 × 3yrs
= Rs. 58,800

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Accountancy Guide Pdf Chapter 3 Accounts of Partnership Firms-Fundamentals Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Accountancy Solutions Chapter 3 Accounts of Partnership Firms-Fundamentals

12th Accountancy Guide Accounts of Partnership Firms-Fundamentals Text Book Back Questions and Answers

I Multiple Choice Questions

Question 1.
In the absence of partnership deed, profits of the firm will be shared by the partners in
(a) Equal ratio
(b) Capital ration
(c) Both (a) and (b)
(d) None of these
Answer:
(a) Equal ratio

Question 2.
In the absence of an agreement among the partners, interest on capital is
(a) Not allowed
(b) Allowed at bank rate
(c) Allowed @ 5% per annum
(d) Allowed @ 6% per annum
Answer:
(a) Not allowed

Question 3.
As per the Indian Partnership Act, 1932, the rate of interest allowed on loans advanced by partners is
(a) 8% per annum
(b) 12% per annum
(c) 5% per annum
(d) 6% per annum
Answer:
(d) 6% per annum

Question 4.
Which of the following is shown in profit and loss appropriation account?
(a) Office Expenses
(b) Salary of staff
(c) Partner’s salary
(d) Interest on bank loan
Answer:
(c) Partner’s salary

Question 5.
When fixed capital method is adapted by a partnership firm, which of the following items will appear in capital account?
(a) Additional capital introduced
(b) Interest on capital
(c) Interest on drawings
(d) Share of profit
Answer:
(a) Additional capital introduced

Question 6.
When a partner withdraws regularly a fixed sum of money at the middle of every month period for which interest is to be calculated on the drawings on an average is
(a) 5.5 moths
(b) 6 months
(c) 12 months
(d) 6.5 months
Answer:
(b) 6 months

Question 7.
Which of the following is the incorrect pair?

Answer:
c

Question 8.
In the absence of an agreement, partners are entitled to
(a) Salary
(b) Commission
(c) Interest on loan
(d) Interest on capital
Answer:
(c) Interest on loan

Question 9.
Pick the odd one out
(a) Partners share profits and losses equally
(b) Interest on partners capital is allowed at 7% per annum
(c) No salary or remuneration allowed
(d) Interest on loan from partners is allowed at 6% per annum
Answer:
(b) Interest on partners capital is allowed at 7% per annum

Question 10.
Profit after interest on drawings, interest on capital and remuneration is ₹ 10,500. Geetha, a partner, is entitled to receive commission @ 5% on profits after charging such commission. Find out commission.
(a) ₹ 50
(b) ₹ 150
(c) ₹ 550
(d) ₹ 500
Hint:

Answer:
(d) ₹ 500

II Very Short Answer Questions

Question 1.
Define partnership.
Answer:
According to Section 4 of the Indian Partnership Act, 1932, the partnership is defined as, “the relation between person who has agreed to share the profits of a business carried on by all or any of them acting for all.

Question 2.
What is a partnership deed?
Answer:
A partnership deed is a document in writing that contains the terms of the agreement among the partners.

Question 3.
What is meant by the fixed capital method?
Answer:
Under the fixed capital method, the capital of the partners is not altered and it remains generally fixed. Two accounts are maintained for each partner namely:

1. Capital account and
2. Current account

The transactions relating to initial capital introduced, additional capital introduced, and capital permanently withdrawn are entered in the capital account and all other transactions are recorded in the current account.

Question 4.
What is the journal entry to be passed for providing interest on capital to a partner? For providing interest on capital.

Question 5.
Why profit and loss appropriation account prepared?
Answer:
The profit and loss appropriation account is an extension of the profit and loss account prepared for the purpose of adjusting the transactions relating to amounts due to and amounts due from partners. It is a nominal account in nature. The balance being the profit or loss is transferred to the partners’ capital or current account in the profit-sharing ratio.

III Short Answer Questions

Question 1.
State the features of partnership?
Answer:
Following are the essential features of a partnership.

1. A partnership is an association of two or more persons. The maximum number of partners is limited to 50.
2. There should be an agreement among the persons to share the profit or loss of the business. The agreement may be oral or written or implied.
3. The agreement must be to carry on a business and to share the profits of the business.
4. The business may be carried on by all the partners or any of them acting for all.

Question 2.
State any six contents of a partnership deed.
Answer:
Contents of partnership deed.
Generally, a partnership deed contains the following:

• Name of the firm and nature and place of business.
• Date of commencement and duration of business.
• Names and addresses of all partners.
• Capital contributed by each partner.
• profit sharing ratio

Question 3.
State the differences between fixed capital method and fluctuating capital method.
Differences between fixed capital method and fluctuating capital method.
Answer:

Question 4.
Write a brief note on the applications of the provisions of the Indian Partnership Act, 1932 in the absence of a partnership deed.
Answer:
Applications of the provisions of the Indian Partnership Act, 1932 in the absence of partnership deed.

1. Remuneration to partners: No salary or remuneration is allowed to any partner. [Section 13(a)]
2. Profit-sharing ratio: Profit and losses are to be shared by the partners equally. [Section 13(b)]
3. Interest on capital: No interest is allowed on the capital. When a partner is entitled to interest on capital contributed as per partnership deed, such interest on capital will be payable only out of profits [Section 13(c)]
4. Interest on loans advanced by partners to the firm: Interest on the loan is to be allowed at the rate of 6 percent per annum. [Section 13(d)]
5. Interest on drawings: No interest is charged on the drawings of the partners.

Question 5.
Jayaraman is a partner who withdrew 10,000 regularly in the middle of every month. Interest is charged on the drawings at 6% per annum. Calculate interest on drawings for the year ended 31st December 2018.
Answer:

IV Exercises

Question 1.
Akash, Bala, Chandru, and Daniel are partners in a firm. There is no partnership deed. How will you deal with the following?

1. Akash has contributed to maximum capital. He demands interest on capital at 10% per annum.
2. Bala has withdrawn ₹ 3,000 per month. Other partners ask Bala to pay interest on drawings @ 8% per annum to the firm. But, Bala did not agree to it.
3. Akash demands the profit to be shared in the capital ratio. But, others do not agree.
4. Daniel demands a salary at the rate of ₹ 10,000 per month as he spends full time for the business.
5. The loan advanced by Chandru to the firm is ₹ 50,000. He demands interest on loan@ 12% per annum

Solution:

1. No interest on capital is payable to any partner.
2. No interest is chargeable on drawings made by the partner.
3. Profits should be distributed equally
4. No remuneration is payable to any partner.
5. Interest on the loan is payable at 6% per annum.

Question 2.
From the following information, prepare capital accounts of partners Rooban and Deri, when their capitals are fixed.
Answer:

Solution :

Question 3.
Arun and Selvam are partners who maintain their capital accounts under fixed capital method. From the following particulars, prepare capital accounts of partners.

Solution :

Question 4.
From the following information, prepare capital accounts of partners Padmini and Padma, When their capitals are fluctuating.

Solution :

Question 5.
Mannan and Ramesh share profits and losses in the ratio of 3:2 and their capital on 1st April 2018 were Mannan ₹ 1,50,000 and Ramesh ₹ 1,00,000 respectively and their current accounts show a credit balance of ₹  25,000 and ₹ 20,000 respectively. Calculate interest on capital at 6% p.a for the year ending 31st March 2019 and show the journal entries.
Solution :
For providing interest on capital

Question 6.
Prakash and Supriya were partners who share profits and losses in the ratio of 5:3. Balance in their capital account on 1st April 2018 was Prakash ₹ 3,00,000 and Supriya ₹ 2,00,000. On 1st July 2018 Prakash introduced additional capital of ₹ 60,000. Supria introduced additional capital of ₹ 30,000 during the year. Calculate on capital at 6% p.a for the year ending 31st March 2019 and show journal entries.
Solution:

Note: Date of introduction of capital by Supria is not given, interest is calculated for an average period of 6 months.

Question 7.
The capital account of Begum and Fatima on 1st January 2018 showed a balance of ₹ 50,000 and ₹ 40,000 respectively. On 1st October 2018, Begum introduced an additional capital of ₹ 10,000 and On 1st May 2018 Fatima introduced an additional capital of ₹ 9,000. Calculate Interest on capital at 4% p.a. for the year ending 31st December 2018.
Solution :

Interest on capital
Begum Rs. 2,100
Fatima Rs. 1,840

Question 8.
From the following balance sheets of Subha and Sudha who share profits and losses in 2:3, Calculate interest on capital at 5% p.a. for the year ending 31st December 2018.

Drawings of subha and sudha during the year were ₹ 8,000 and ₹ 10,000 respectively. Profit earned during the year was ₹ 30,000.
Solution :

Question 9.
From the following balance sheets of Rajan and Devan who share profits and losses in 2:1, Calculate interest on capital at 6% p.a. for the year ending 31st December 2018.

on 1st April, Rajan introduced an additional capital of ₹ 40,000, and on 1st September 2018. Devan introduced ₹ 30,000. Drawings of Rajan and Devan during the year were ₹ 20,000 and ₹ 10,000 respectively. Profit earned during the year was ₹ 70,000
Solution :

Interest on Capital

Interest on capital
Rajan = Rs. 5,400
Devan = Rs. 3,600

Question 10.
Ahmad and Basheer Contribute ₹ 60,000 and ₹ 40,000 respectively as capital. Their respective share of profit is 2:1 and the profit before interest on capital for the year is ₹ 5,000. Computer the amount of interest on capital in each of the following situations:

1. If the partnership deed is silent as to the interest of capital
2. If interest on capital @ 4% is allowed as per the partnership deed
3. If the partnership deed allows interest on capital @ 6% per annum.

Solution
interest on capital @ 4%
Ahamed = 60,000 × \(\frac{4}{100}\) = 2,400
Basheer = 40,000 × \(\frac{4}{100}\) = 1,600

interest on capital @ 6%
Ahamed = 60,000 × \(\frac{6}{100}\) = 3,600
Basheer = 40,000 × \(\frac{6}{100}\) = 2,400

1. No Interest on capital is allowed
2. Since there is sufficient profit, interest on capital wifi be provided Ahamad. ₹ 2,400; Basheer. ₹ 1,600
3. Since the profit is insufficient, interest on capital will not be provided. profit of ₹ 5,000 will be distributed to the partners in their capital ratio of 3:2

Question 11.
Mani is a partner, who withdrew ₹ 30,000 on 1st September 2018. Interest on drawings is charged at 6% per annum. Calculate interest on drawings on 31st December 2018 and show the journal entries by assuming that the fluctuating capital method is followed.
Solution :

Question 12.
Santhosh is a partner in a partnership firm. As per the partnership deed, interest on drawings is charged per annum. During the year ended 31st December 2018 he withdrew as follows:

calculate the amount of interest on drawings.
Solution :

Question 13.
Kumar is a partner in a partnership firm. As per the partnership deed, interest on drawings is charged at 6% per annum. During the year ended 31st December 2018 he wi drew as follows:

calculate the amount of interest on drawings.
Solution :

Question 14.
Mathew is a partner who withdrew ₹ 20,000 during the year 2018. Interest on drawings is charged at 10% per annum. Calculate interest on drawings on 31st December 2018.
Solution :

Note: Date of withdrawal is not given, interest is calculated for an average period of 6 months.

Question 15.
Santhosh is a partner in a partnership firm. As per the partnership deed, interest on drawings is charged at 6% per During the ended 31st December 2018 he withdrew as follows:

calculate the amount of interest on drawings by using the product method.
Solution :

Question 16.
Kavitha is a partner in a firm. She withdraws ₹ 2,500 p.m. regularly interest on drawings is charged @ 4% p.a. Calculate the interest on drawings using average period, if she draws.
(i) at the beginning of every month
(ii) in the middle of every month
(iii) at the end of every month

Solution :
(i) at the beginning of every month
Amt withdrawn = 2,500 × 12 = Rs. 30,000

Question 17.
Kevin and Francis are partners. Kevin draws ₹ 5,000 at the end of each quarter. Interest on drawings is chargeable at 6% p.a. Calculate interest on drawings for the year ending 31st March 2019 using the average period.
Solution:
Kevin → Rs. 5,000 → at the end of each quarter
Average period = \(\frac{9+0}{2}=4 \frac{1}{2}\) Months
Amt withdrew = 5000 × 4 times = Rs. 20,000
IOD = 20,000 × \(\frac{6}{100} \times \frac{9}{24}\)= Rs. 450

Question 18.
Ram and Shyam were partners. Ram withdrew ₹ 18,000 at the beginning of each half year. Interest on drawings is chargeable @ 10% p.a. Calculate interest on the drawings for the year ending 31st December 2018 using the average period.
Solution :
Ram → Rs. 18,000 → beg of each half year.
Average period = \(\frac{12+6}{2}\) = 9 months
Amount withdrawn = 18,000 × 2 times = Rs. 36,000
IOD = 36,000 × \(\frac{10}{100} \times \frac{9}{12}\)= Rs. 2,700

Question 19.
Janani, Kamali, and Lakshmi are partners in the firm sharing profits and losses equally. As per the terms of the partnership deed, Kamali allows a monthly salary of ₹ 10,000, and Lakshmi is allowed a commission of ₹ 40,000 per annum for their contribution to the business of the firm. You are required to pass the necessary journal entry. Assume that their capitals are fluctuating.
Solution :

Question 20.
Sibi and Manoj are partners in a firm. Sibi is to get a commission of 20% of net profit before charging any commission. Manoj is to get a commission of 20% on net profit after charging all commission. Net profit for the year ended 31st Dec 2018 before ch y commission was ₹ 60,000. Find the commission of Sibi and Man Also show the distribution of profit.
Solution:

Note: Assumed to be equal partners (1:1)

Question 21.
Anand and Narayanan are partners in firm sharing profits and losses in the ratio of 5:3 On 1st January 2018, their capitals were ₹ 50,000 and ₹ 30,000 respectively. The partnership deed specifies the following:
(a) Interest on capital is to be allowed at 6% per annum.
(b) Interest on drawings charged to Anand and Narayanan are ₹ 1,000 and ₹ 800 respectively.
(c) The net profit of the firm before considering interest on capital and interest on drawings amounted to ₹ 35,000
Give necessary journal entries and prepare profit and loss appropriation account as on 31st December 2018. Assume that the capitals are fluctuating.
Solution :

Question 22.
Dinesh and Sugumar entered into a partnership agreement on 1st January 2018, Dinesh contributing ₹ 1,50,000 and Sugumar ₹ 1,20,000 as capital. The agreement provided that:
(a) Profits and losses shared in the ratio 2:1 as between Dinesh and Sugumar.
(b) Partners to be entitled to interest on capital @ 4% p.a
(c) Interest on drawings to be charged Dinesh: ₹ 3,600 and Sugumar: ₹ 2,200
(d) Dinesh to receive a salary of ₹ 60,000 for the year, and
(e) Sugumar to receive a commission of ₹  80,000
During the year ended on 31st December 2018, the firm made a profit of ₹ 2,20,000 before adjustment of interest, salary and commission.
Prepare the Profit and loss appropriation account.
Solution :

Question 23.
Antony and Ranjith Started a business on 1st April 2018 with capitals of ₹ 4,00,000 and ₹ 3,00,000 respect According to the Partnership Deed, Anton is to get the salary of ₹ 90,000 per annum, Ranj ith is got 25% commission on profit after allowing salary to Antony and interest on capital @ 5% p.a but before charging such commission. The profit-sharing ratio between the two partners is 1:1 During the year, the firm earned a profit of ₹ 3,65,000.
Prepare profit and loss appropriation account. The firm closes its accounts on 31st March every year.
Solution :

Calculation of profit before charging such commission
Net profit 3,65,000
Less: Ioc 20,000+15,000
salary 90,000 1,25,000
Profit before Commission 2,40,000
Commission = Net profit before commission × \(\frac{\text { Rate }}{100}\)
= 2,40,000 × \(\frac{25}{100}\)
= Rs.60,000

12th Accountancy Guide Accounts of Partnership Firms-Fundamentals Additional Important Questions and Answers

Question 1.
The minimum number of Reasons in a partnership firm is
(a) One
(b) Two
(c) Three
Answer:
(b) Two

Question 2.
In a partnership business, the agreement is
(a) Compulsory
(b) Optional
(c) Not necessary.
Answer:
(a) Compulsory

Question 3.
In a partnership, partners share their profits & losses in ‘ ratio
(a) their capital
(b) equal
(c) agreed
Answer:
(c) agreed

Question 4.
under fixed capital system, the profits and losses of partners will be transferred to their account
(a) Current
(b) Drawings
(c) Capital
Answer:
(a) Current

Question 5.
Interest on capital is calculated on the
(a) Opening capital
(b) Closing capital
(c) Average capital
Answer:
(a) Opening capital

Question 6.
Current accounts for partners will be opened under
(a) fixed capital method
(b) fluctuation capital method
(c) either fixed capital method or fluctuating capital method
Answer:
(a) fixed capital method

Question 7.
In the absence of agreement profits and losses are divided
(a) in the ratio of capitals
(b) in the ratio of time devoted by each partner
(c) equally
Answer:
(c) equally

Question 8.
x and y are partners sharing the profits and losses in the ratio of 2:3 with capitals of Rs. 1,20,000 and Rs. 60,000 respectively profits for the year are Rs. 9,000. If the partnership deed is silent as to interest on the capital show how profit is shared among x and y
(a) profit x – Rs.6,000 y – Rs.3,000
(b) profit x – Rs.3,600 y – Rs.5,400
(c) profit x – Rs.3,000 y – Rs. 6000
Hint:
Profit ₹ 9,000 Sharing ratio = 2:3
X Partner profit = 9,000 × 2/5 = ₹ 3,600
Y Partner profit = 9,000 × 3/5  = ₹ 5,400
Answer:
(b) profits – Rs.3,600 y – Rs.5,400

Question 9.
where a partner is entitled to interest on capital such interest will be payable
(a) Only out of profits
(b) Only out of Capital
(c) Out of profits or out of capital
Answer:
(a) Only out of profits

Question 10.
under fixed capital method, salary payable to a partner is recorded
(a) in the current account
(b) in capital account
(c) either in current account or capital account
Answer:
(a) in the current account

II Very Short Answer Questions

Question 11.
What is meant by the fluctuating capital method?
Answer:
Under this method, only a capital account is maintained for each partner. All the transactions between the partner and the firm are recorded in the capital account. This account is credited with the initial and additional capital introduced by the partner. The account is debited with capital withdrawn, drawings, interest on drawings, and share of loss of the partner. As a result, the balance in this account goes on fluctuating periodically. Under this method, the partner s capital account may show either credit balance or debit balance.

Question 12.
Mention the methods of calculating interest on drawings?
Answer:

1. Direct Method
2. Product Method
3. Average period Method.

Question 13.
How to calculate the average period under different circumstances?
Answer:
The average period is computed as follows:
The following table shows the average period in months for withdrawal made at the beginning. In the middle and at the end of every month, quarter and half- year of the year.

Additional problems:

Question 14.
Show how the following items will appear in the capital accounts of the partners, Anbu and Balu.

Solution :
a) When capital accounts are fixed:

b) when capital accounts are fluctuating:

capital Accounts

Question 15.
Write up the capital and. current accounts of the partners, Kala and Mala from the following and show how these will appear in the Balance Sheet.

Solution :

Question 16.
Ravi and Raghu started business on April 1, 2003, with a capital of 90,000 and Rs. 70,000 respectively. Ravi introduced Rs. 10,000 as additional capital on July 1, 2003. Interset on capital is to be allowed @ 10%. Calculate the interest payable to Ravi and Raghu for the year ending March 31, 2004.
Solution :

Question 17.
P, Q and R were partners sharing profits in the ratio of 3:2:1. P draws Rs.5,000 at the end of each quarter. Q draws Rs. 10,000 at the end of each half-year. R draws Rs.2,000 on 1.5.2004 Rs.3,000 on 31.10.2004, Rs.5,000 on 30.11.2004. Calculate interest on their drawings at 10% p.a for the year ending 31.3.2005.
Solution :
Calculation of interest on Drawings under Product Method:
a) Interest on drawing of P :

Interest on drawings at 10% p.a. on Rs.90,000
Interst on drawings = 90,000 × \(\frac{10}{100} \times \frac{1}{12}\) = Rs. 750
Interest on drawings of Q:

Interest on drawings at 10% p.a. on Rs.60,000
Interst on drawings = 60,000 × \(\frac{10}{100} \times \frac{1}{12}\) = Rs.500
Interst on drawings of R:

Interest on drawings at 10% p.a. on Rs.57,000
Interest on drawings = 57,000 x \(\frac{10}{100} \times \frac{1}{12}\) = Rs.475

Question 18.
Mahesh and Ramesh are partners sharing profits in the ratio of 3:2 with capitals of Rs.50,000 and Rs.40,000 respectively. Interest on capital is agreed at 8%p.a Interest on drawings is fixed at 10% p.a. The drawings of the partners were Rs.15,000 and Rs.10.000, the interest for Mahesh Rs.750 and for Ramesh Rs.500. Mahesh is entitled to a salary of Rs. 12,000 p.a. and Ramesh is entitled to get a commission of 10% on the Net Profit before charging such cc ion. The Net Profit of the firm before making the above adjustments was Rs.60,000 for the year ended 31st March 2005.
Prepare the profit and loss appropriation account.
Solution :
In the Books of the Firm Profit and Loss Appropriation Account

Note: Calculation of commission.
Step 1→ Total the credit side of the Profit and Loss Appropriation Account, i.e., Rs. 61,250
Step 2 → Total the debit side of the Profit and Loss Appropriation Account, i.e., Rs. 19,200
Step 3 → Find the balance, i.e., Rs. 42,050.
Step 4 → Apply the formula.
Commission = Net Profit before commission × \(\frac{\text { Rate of Commission }}{100} \text {\)
Commission = 42,050 × \(\frac{10}{100}\) = 4,205
The Balance of Rs. 37,845 (Rs.42,050 – Rs. 4,205) is transferred to Parnters Capital accounts in the ratio.

Question 19.
X and Y are partners in a firm, sharing profits losses equal. X is entitled to a salary of Rs. 5,000 p.m. Y is entitled to a con ion c 0% of Net Profit after charging such commission. Net Profit before charging commission and salary was Rs. 1,48,000. Show the Profit and loss appropriation account.
Solution:
a) Calculation of Salary to X:
5,0 p.m. for 12 months = 12 × 5,000 = Rs. 60,000
Calculation of Commission to Y:
Percentage of Net profit after charging the commission =
Net Profit before commission × \(\frac{\text { Rate of commission }}{100+\text { Rate of commision }}\)
Net Profit before commission = 1,48,000 – 60,000 = Rs.88,000
Commission = 88,000 × \(\frac{10}{100+10}\)
= 88,000 × \(\frac{10}{110}\)
= Rs.8,000

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 9 Applications of Integration Ex 9.6 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.6

Question 1.
Evaluate the following
(i) \(\int_{0}^{π/2}\) sin¹⁰x dx
Solution:
Here n = 10, which is even

(ii) \(\int_{0}^{π/2}\) cos⁷x dx
Solution:
Here n = 7, which is odd

(iii) \(\int_{0}^{π/4}\) sin⁶ 2x dx
Solution:
put t = 2x
dt = 2 dx

(iv) \(\int_{0}^{π/6}\) sin⁵ 3x dx
Solution:
put t = 3x
dt = 3 dx

(v) \(\int_{0}^{π/2}\) sin² x cos⁴ x dx
Solution:
Here m = 2, which is even and n = 4, which is even

(vi) \(\int_{0}^{2π}\) sin⁷ \(\frac{x}{4}\) dx
Solution:

(vii) \(\int_{0}^{π/2}\) sin³ θ cos⁵ θ dθ
Solution:

Aliter Method

(viii) \(\int_{1}^{0}\) x² (1 – x)³ dx
Solution:
By applying reduction formula

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 9 Applications of Integration Ex 9.4 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.4

Question 1.
Evaluate the following
\(\int_{0}^{1}\) x³e^-2x dx
Solution:
Bernoulli’s formula,
∫uv dx = uv₁ – u¹v₂ + u²v₃ – u³v₄ + ….

Question 2.
\(\int_{0}^{1}\) \(\frac{sin(3tan^{-1}x)tan^{-1}x dx}{1+x^2}\)
Solution:

Question 3.
\(\int_{0}^{1/√2}\) \(\frac{e^{sin^{-1}x}sin^{-1}x}{\sqrt{1-x^2}}\) dx
Solution:

Question 4.
\(\int_{0}^{\pi / 2}\) x² cos 2x dx
Solution:

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 9 Applications of Integration Ex 9.3 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 9 Applications of Integration Ex 9.3

Question 1.
Evaluate the following definite integrals.
(i) \(\int_{3}^{4}\) \(\frac{dx}{x^2-4}\)
Solution:

(ii) \(\int_{-1}^{1}\) \(\frac{dx}{x^2+2x+5}\)
Solution:

(iii) \(\int_{0}^{1}\) \(\frac{\sqrt{1-x}}{\sqrt{1+x}}\) dx
Solution:

(iv) \(\int_{0}^{\pi / 2}\) (\(\frac{1+sin}{1+cosx}\))dx
Solution:

(v) \(\int_{0}^{\pi / 2}\) \(\sqrt{cos θ}\) sin³θ dθ
Solution:

(vi) \(\int_{0}^{1}\) \(\frac{1-x^2}{(1+x^2)^2}\) dx
Solution:

Question 2.
Evaluate the following integrals using properties of integration:
(i) \(\int_{-5}^{5}\) x cos (\(\frac{e^x-1}{e^x+1}\)) dx
Solution:

(ii) \(\int_{-\pi / 2}^{\pi / 2}\) (x⁵ + x cos x + tan³ x) dx
Solution:
\(\int_{-\pi / 2}^{\pi / 2}\) (x⁵ + x cos x + tan³ x) dx
= \(\int_{-\pi / 2}^{\pi / 2}\) (x⁵ + x cos x + tan³ x) dx + \(\int_{-\pi / 2}^{\pi / 2}\)
Let f(x) = x⁵ + x cos x + tan³x
f(-x) = -x⁵ – x cos x – tan³x
f(x) = -f(-x)
f(x) is an odd function

(iii) \(\int_{-\pi / 4}^{\pi / 4}\) sin² x dx
Solution:
I = \(\int_{-\pi / 4}^{\pi / 4}\) sin² x dx
f(x) = sin²x
f(-x) = sin²(-x) = sin²x
f(x) = f(-x)
f(x) is an even function

(iv) \(\int_{0}^{2π}\) x log(\(\frac{3+cos x}{3-cos x}\))dx
Solution:

(v) \(\int_{0}^{π}\) sin⁴ x cos³ x dx
Solution:
\(\int_{0}^{π}\) sin⁴ x cos³ x dx
f(x) = sin⁴x cos³x
f(2π – x) = sin⁴(2π – x) cos³ (2π – x)
= sin⁴x cos³x
f(2π – x) = f(x)

Limit from 0 to π tends to 0 to 0
∴ Integral value = 0
∴ \(\int_{0}^{π}\) sin⁴ x cos³ x dx = 0

(vi) \(\int_{0}^{1}\) |5x – 3|dx
Solution:

(vii) \(\int_{0}^{sin^2x}\) sin^-1 √t dt + \(\int_{0}^{cos^2x}\) cos^-1 √t dt
Solution:
I₁ = \(\int_{0}^{sin^2x}\) sin^-1 √t dt
Put sin^-1 √t = θ
√t = sin θ
\(\frac{1}{2√t}\) dt = cos θ dθ
dt = 2√t cos θ dθ
= 2 sin θ cos θ dθ
dt = sin 2θ dθ

I₁ = \(\int_{0}^{cos^2x}\) cos^-1 √t dt
Put cos^-1 √t = θ
√t = cos θ
\(\frac{1}{2√t}\) dt = -sin θ dθ
dt = -2√t sin θ dθ
= -2 cos θ sin θ dθ
dt = -sin 2θ dθ

(viii) \(\int_{0}^{1}\) \(\frac{log(1+x)}{1+x^2}\) dx
Solution:

(ix) \(\int_{0}^{π}\) \(\frac{x sin x}{1+sin x}\) dx
Solution:

(x) \(\int_{π/8}^{3π/8}\) \(\frac{1}{1+\sqrt{tan x}}\) dx
Solution:

(xi) \(\int_{0}^{π}\) x[sin²(sin x) + cos² (cos x)] dx
Solution:
Let I = \(\int_{0}^{π}\) x[sin²(sin x) + cos² (cos x)] dx
f(x) = sin² (sin x) + cos² (cos x)
f(π – x) = sin² (sin π – x)) + cos² (cos(π – x))
= sin² (sin x) + cos² (cos x)
f(x) = f(π – x)

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Accountancy Guide Pdf Chapter 2 Accounts of Not-For-Profit Organisation Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Accountancy Solutions Chapter 2 Accounts of Not-For-Profit Organisation

12th Accountancy Guide Accounts of Not-For-Profit Organisation Text Book Back Questions and Answers

I Multiple Choice Questions

Choose the correct answer

Question 1.
Receipts and payments account is a
(a) Nominal A/c
(b) Real A/c
(c) Personal A/c
(d) Representative personal account
Answer:
(b) Real A/c

Question 2.
Receipts and payments account records receipts and payments of
(a) Revenue nature only
(b) Captital nature only
(c) Both revenue and captial nature
(d) None of the above
Answer:
(c) Both revenue and captial nature

Question 3.
Balance of receipts and payments account indicates the
(a) Loss incurrd during the period
(b) Excess of income over expenditure of the period
(c) Total cash payments during the period
(d) Cash and bank balance as on the date
Answer:
(d) Cash and bank balance as on the date

Question 4.
Income and expenditure account is a
(a) Nominal A/c
(b) Real A/c
(c) Personal A/c
(d) Representative personal account
Answer:
(a) Nominal A/c

Question 5.
Income and expenditure Account is prepared to find out
(a) Profit or loss
(b) Cash and bank balance
(c) Surplus or deficit
(d) Financial position
Answer:
(c) Surplus or deficit

Question 6.
Which of the following should not be recorded in the income and expenditure account?
(a) Sale of old news papers
(b) Loss on sale of asset
(c) Honorarium paid to the secretary
(d) Sale proceeds of furniture
Answer:
(d) Sale proceeds of furniture

Question 7.
Subsceiption due but not received for the current year is
(a) An asset
(c) An expense
(b) A liability
(d) An item to be ignored
Answer:
(a) An asset

Question 8.
Legacy is a
(a) Revenue expenditure
(b) Capital expenditure
(c) Revenue receipt
(d) Capital receipt
Answer:
(d) Capital receipt

Question 9.
Donations received for a specific purpose is
(a) Revenue receipt
(b) Capital receipt
(c) Revenue expenditure
(d) Capital expenditure
Answer:
(b) Capital receipt

Question 10.
There are 500 members in a club each paying ₹ 100 as annual subscription. Subscription due but not received for the current year is ₹ 200; Subscription received in advance is ₹ 300. Find out the amount of subscription to be shown in the income and expend ; account.
(a) ₹ 50,500
(b) ₹ 50,200
(c) ₹ 49,900
(d) ₹ 49,800
Hint:

Answer:
(a) ₹ 50,500

II Very Short Answer Questions

Question 1.
State the meanting of not-for-profit organisation.
Answer:
Some organisations are established for the purpose of rendering servies to the public without any profit motive. They may be created for the promotion of art, culture, education, sports, etc. These organisations are called not-for-profit organisation.

Question 2.
What is receipts any payments account?
Answer:
Receipts and Payments account is a summary of cash and bank transactions of not-for- profit organisations prepared at the end of eac financial year.

It is a real account in nature. The receipts any payments account begins with the opening balances of cash and bank and ends with closing balances of cash and bank. All cash receipts are shown on the debit side and all cash payments are shown on the credit side of this account. All cash receipts and cash payments whether of capital or revenue nature will be recorded irrespective of the period for which the amoutn is received or paid, it is recorded if cash is received or paind during the year.

Question 3.
What is Legacy?
Answer:
A gift made to a not-for-profit organisation by a will, is called legacy. It is a capital receipt.

Question 4.
Write a short note on life membership fees.
Answer:
Amount received towards life membership fee from members is a capital receipt as it is non-recurring in nature.

Question 5.
Give four examples for Capital r pts of not-for-profit organisation.
Answer:
Life membership fees, Legacies Specifi, Specific donations, Sale of fixed assets, Special funds, Tournament fund prize

Question 6.
Give four examples for revenue receipts of not-for-profit organisation?
Answer:
Subscription, Interest on investment, Interest on fixed deposit
Sale of (old) sports materials, Sale of (old) newspapers

III Short Answer Questions

Question 1.
What is income and expenditure account?
Answer:
Income and expenditure account is a summary of income and expenditure of a not-for- profit organisation prepared at the end of an accounting year. It is prepared to find out the surplus or deficit pertaining to a particular year.
It is a nominal account in nature in which items of revenue receipts and revenue expenditure, relating to the current year alone are recorded. It is prepared following the accrual basis of accounting.

Question 2.
State the differences between Receipts and Payments Account and Income and Expenditure Account.
Answer:

Question 3.
How annual subscription is dealt with in the final accounts of not-for-profit organisation?
Answer:

Question 4.
How the following items are dealt with in the final accounts of not-for-profit organisation? (a) Sale of sports materials (b) Life membership fees (c) Tournament fund
Answer:

• Sale of sports materials: Shown on the credit side of Income & Edpenditure A/c.
• Life membership fees: being capital receipt, will be shown on the liability side of the B/s.
• Tournament Fund: being capital receipt, will be shown on the liability side o f the B/s.

IV Exercise

Question 1.
From the information given below, prepare Receipts and Payments account of Kurunji Sports Club for the year ended 31st December, 2018

Solution :
In the books of Kurunji Sports Club Receipts & Payments A/c for the year ended 31.12.2018
Answer:

Cash balance: ₹ 5,000

Question 2.
From the information given below, prepare Receipts and Payments account of Coimbatore Cricket club for the year ending 31st March, 2019.

Solution:
In the book of Coimbatore Cricket Club/Receipts & Payments A/c for the year ended 31.3.2019

Answer:
Bank balance: ₹ 2,400

(Hint: Wages yet to be paid is a non cash item. Hence, it is excluded in receipts and payments account)

Question 3.
From the information given below, prepare Receipts and Payments account of Madurai Mother Theresa Mahalir Madram for the year ended 31st December, 2018.

Solution: In the book of Mother Teresa Mahalir Mandram, Madurai Receipt & Payment A/c for the year ended 31.12.2018

Answer:
Bank Overdraft: ₹ 4,700
(Hint: As depreciation on furniture is a non cash item, it is excluded in receipts and payments account)

Question 4.
Mayiladuthrai Recreation Club gives you the following details. Prepare Receipts and Payments account for the year ended 31st March, 2019.

Solution:
In the books of Mayiladuthurai Recreation Club Receipts & Payments A/c for the year ended 31.3.2019


Answer:
Bank balance: ₹ 50,000

Question 5.
From the following information, prepare Receipts and Payments account of Cuddalore Kabaddi Association for the year ended 31st March, 2019

Solution :
In the books of Cuddalore Kabaddi Association
Receipts & Payments A/c for the year ended 31.3.2019

Answer:
Bank Overdraft: ₹ 4,500

Question 6.
From the following receipts and payments account of Tenkasi Ihiruvalluvar Mandram, Prepare income and expenditure account for the year ended 31st March, 2019.

In the books of Tenkasi Ihiruvalluvar Mandram Income &Expenditure A/c for the year ended 31.3.19


Answer:
Surplus: ₹14,000

Question 7.
From the following receipts and payment account, prepare income and expenditure account of Kumbakonam Basket Ball Association for the year ended 31st March, 2018.

Solution: In the books of Kumbakonam Basket Ball Association Income &Expenditure A/cfor the year ended 31.3.18

Answer:
Deficit: ₹ 26,000

Question 8.
From the following receipts and payments account and the additional information given below, calculate the amoumt of of subscription to be shown in Income and expenditure account for the year ending 31st December, 2018.

Additional information: Subscription outstanding for the year 2018 is Rs.8,000
Solution:
Income & Expenditure A/c for the year ended 31.12.2018

Answer:
Subscription for 2018: ₹ 1,80,000)

Question 9.
How the following items will appear in the final accounts of a club for the year ending 31st March 2019?

There are 200 members in the club each paying an annual subscription of ₹ 400 per annum. Subscription still outstanding for the year 2017-2018 is ₹ 2,000.
Solution :

Answer:
Income and Expenditure A/c: Subscription: ₹ 80,000 Balance Sheet: Assets: Subscription outstanding: ₹ 32,000; Liabilities: Subscription received in advance: ₹ 5,000

Question 10.
Ho w will the following items appear in the final accounts of a club for the year ending 31st March 2017? Received subscription of ₹ 40,000 during the year 2016-17. This includes subscription of ₹ 5,000 for 2015-16 and ₹ 3,000 for the year 2017-18. subscription of ₹ 1,000 is still outstanding for the year 2016-17.
Solution:
Income & Expenditure A/c for the year ended 31.3.17

Answer:
Income and Expenditure A/c: Subscription: ₹ 33,000
Balance Sheet: Assets: Subscription outstanding: ₹ 1,000;
Liabilities: Subscription received in advance: ₹ 3,000

Question 11.
Compute income from subscription for the year 2018 from the following particulars relating to a club.

Subscription received during in the year 2018: ₹ 45,000
Solution:
Calculation of income from subscription for the year 2018

Answer:
Income and Expenditure A/c: Subscription: ₹ 44,000

Question 12.
From the following particulars, show how the item ‘Subscription’ will appear in the Income and Expenditure Account for the year ended 31.12.2018?

Subscription received in 2018 is ₹ 50,000 which includes ₹ 5,000 for 2017 and ₹ 7,000 for 2019. Subscription outstanding for the year 2018 is ₹ 6,000. Subscription of ₹ 4,000 was received in advance for 2018 in the year 2017.
Solution:
Income & Expenditure A/c for three year ended 31.12.18

Answer:
Income and Expenditure A/c: Subscription:₹ 48,000

Question 13.
How the following items appear in the final accounts of Thoothukudi Young Pioneers Association?
There are one hundred members in the association each paying 25 as annual subscription. By the end of the year 10 members had not paid their subscription but four members had paid for the next year in advance.
Solution:
Calculation of income from subscription

Answer:
Income and Expenditure Account: Subscription: ₹ 2,500
Balance Sheet: Assets: Subscription outstanding: ₹ 250;
Liabilities: Subscription received in advance: ₹ 100

Question 14.
How will the following appear in the final accounts of Marthadam Women Cultural Association?

Solution :
Income & Expenditure A/c for the year ended 31.3.2019

Answer:
Income and Expenditure Account (Dr): ₹ 90,000;
Balance Sheet: Assets: Stock of sports materials: ₹ 10,000

Question 15.
How will the following appear in the final accounts of Vedaranyam Sports Club?

Solution:
Income & Expenditure A/c for the year ended

Answer:
Income and Expenditure Account: Bats and balls consumed : ₹ 16,000 (Dr);
Sale of old sports materials: ₹ 2,000 (Cr.)
Balance Sheet: Assets side: Stock of bats and balls: ₹ 4,000)

Question 16.
Show how the following items appear in the income and expenditure account of Sirkazhi Singers Association?

Solution:
Income & Expenditure A/c for the year ended 31.3.2018

Answer:
Stationery consumed : ₹ 6,900 (Dr.)

Question 17.
Chennai tennis club had Match fund showing credit balance of ₹ 24,000 on 1st April, 2018. Receipt to the fund during the year was ₹ 26,000. Match expensed incurred during the year was ₹ 33,000. How these items will appear in the final accounts of the club for the year ended 31st March, 2019?
Solution:
Balance Sheet As on 31.3.19

Answer:
Balance sheet: Liabilities: Match fund : ₹ 17,000

Question 18.
How will the following appear in the final accounts of Karaikudi sports club for the year ending 31st March, 2019?
Particulars ?

Solution:
Balance Sheet As on 31.3.2019

Answer:
Balance sheet: Liabilities: Tournament fund: ₹ 49,000
Assets: Tournament fund investment: ₹ 90,000

Question 19.
Compute capital fund of Salam Sports Club as on 01.4.2019?

Solution:
Balance Sheet As on 1.4.2019

Answer:
Capital fund: ₹ 80,000

Question 20.
From the follwoing Receipts and Paymentaccount and from the information given below of Ramanathapuram Sports Club, prepare Income and Expenditure account for the year ended 31st December, 2018 and the balance sheet as on that date.

Additional information:
(i) Capital fund as on 1st January 2018 ₹ 30,000
(ii) Opening stock of sports material ₹ 3,000 and closing stock of sports material ₹ 5,000
Solution
Dr. Income & Expenditure A/c for three year ended 31.12.18

Answer:
Surplus: ₹ 2,300; Balance Sheet total: ₹ 48,300

Question 21.
From the following Receipts and Payments account of Yarcaud Youth Association, prepare Income and expenditure account for the year ended 31st March, 2019 and the balance sheet as on the date.

Additional information:
(i) Opening capital fund ₹ 20,000.
(ii) Stock of books on 1.4.2018 ₹ 9,200.
(iii) Subscription due but not received ₹ 1,700.
(iv) Stock of stationery on 1.4.2018 ₹ 1,200 and stock of stationery on 31.3.2019, ₹ 2,000
Solution:
Income & Expenditure A/c for the year ended 31.3.19

Answer:
Surplus: ₹ 7,800; Balance Sheet total: ₹ 37,800

Question 22.
Following is the Receipts and Payments account of Neyveli Science Club for the year ended 31st December, 2018.
i
Additional information:
(i) Opening capital fund ₹ 6,400.
(ii) Subscription includes ₹ 600 for the year 2019.
(iii) Science equipment as on 1.1.2018 ₹ 5,000.
(iv) Surplus on account of exhibition should be kept in reserve for new auditorium. Prepare income and expenditure account for the year ended 31st December, 2018 and the balance sheet as on that date.
Solution:
Income & Expenditure A/c for the year ended 31.12.18

Answer:
Deficit: ₹ 1,400; Balance Sheet total: ₹ 10,600

Question 23.
From the following Receipts and Payments account of Sivasasi Pensioner’s Recreation Club, prepare income and expenditure account for the year ended 31st March, 2018 and the balance sheet as on that date.

Additional information:
(i) The club had 300 members each paying ₹ 100 as annual subscription.
(ii) The club had furniture ₹ 10,000 on 1.4.2017.
(iii) The subscription still due but not received for the year 2016 – 2017 is ₹ 1,000.
Solution:
Income & Expenditure A/c for thre year ended 31.3.18

Answer:
Surplus: ₹ 4,000; Opening capital fund ₹ 46,000; Balance sheet total: ₹ 99,000

Question 24.
Following is the Receipts and payments account ofVirudhunagar Volleyball Association for the year ended 31st December, 2018.

Additional information:
(i) On 1.1.2018, the association owned investments ₹ 10,000, premises and grounds ₹ 40,000, stock of bats and balls ₹ 5,000.
(ii) Subscription 15,000 related to 2017 is still due.
(iii) Subscription due for the year 2018, ₹ 6,000.
Prepare income and expenditure account for the year ended 31st December, 2018 and the balance sheet on that date.
Solution :
Balance Sheet As on 1.1.2018


Answer:
SurpIus: ₹ 52,000; Opening capital fund ₹ 75,000;
Closing balance sheet total: ₹ 1,32,000

12th Accountancy Guide Accounts of Not-For-Profit Organisation Additional Important Questions and Answers

I Multiple Choice Questions

Question 1.
Receipts & payments A/c records receipts & payments of
(a) Current year only
(b) Previous & future period only
(c) both a & b
Answer:
(c) both a & b

Question 2.
Non-cash items such as depreciation outstanding expenses and accrued income are not shown in
(a) Receipts & payments A/c
(b) Income & expenditure A/c
(c) Balance sheet
Answer:
(a) Receipts & payments A/c

Question 3.
Only revenue items are recorded in
(a) Income & Expenditure A/c
(b) Receipts & payments A/c
(c) Balance sheet
Answer:
(a) Income & Expenditure A/c

Question 4.
Interest on investment received is a
(a) Capital receipt
(b) revenue receipt
(c) Capital Expenditure
Answer:
(b) revenue receipt

Question 5.
Grants received towards construction of buildings acqisiton of assets etc are treated as
(a) Capital receipt
(b) Capital expenditure
(c) Revenue Receipt
Answer:
(a) Capital receipt

Question 6.
Grants received towards maintenance of assets, payments of salaries etc aire are treated as
(a) Capital receipt
(b) revenue receipt
(c) Capital Expenditure
Answer:
(b) revenue receipt

Question 7.
Revenue items of current year alone are recorded in
(a) Receipts & Payments A/c
(b) Income & Expenditure A/c
(c) Balance sheet
Answer:
(b) Income & Expenditure A/c

III. Short Answer Questions

Question 1.
What are the ffeatures of not-for-profit organisations.
Answer:
Following are the features of not-for-profit organisations:

1. Not-for-profit organisations are the organisations which function without any profit motive.
2. Their main aim is to provide services to a specific group or the public at large.
3. Generally, they do not undertake business or trading activities.
4. Their main sources of income include subscription from members, donations, grant-in¬aid and legacies.

Question 2.
What are the accounts prepared by not-for-profit organisations
Answer:

1. Receipts and payments account,
2. Income and expenditure account and
3. Balance sheet

Question 3.
What are the steps in the preparation of Receipts & Payments A/c?
Answer:
Following are the steps involved in the preparation of receipts and payments account:

• Record the opening balance of cash in hand and favourable bank balance on the debit side of receipts and payments account. If there is bank overdraft, it must be recorded on the credit side.
• Actual cash receipts during the year are recorded on the debit side and actual cash payments during the year are recorded on the credit side.
• While recording cash receipts and payments, no distinction needs to be made between revenue and capital items. Similarly, no distinction needs to be made whether the amount reveived or paid relates to the current period, previous period or future period.
• If the total of the debit side is more than the credit side, the balancing figure will appear on the credit side. It represents the closing balance of cash or bank.
• If the total of the credit side is more than the debit side, the balancing figure will appear on the debit side. It represents bank overdraft.

Question 4.
Name a few examples capital for expenditure & revenue expenditure.
Answer:

IV Additional Problems:

Question 1.
The following particulars of a club are available.

Prepare Receipts and Payments Account as on 31st March, 2002.
Solution:
Receipts and Payments A/c for the year ended 31st March, 2002

Question 2.
From the following particulars prepare receipts and payments account of a club for the year 2000:
Cash Balance (1st Jan. 2001) Rs. 4,000; Entry fee received Rs. 400; Subscription received Rs. 800; Last year’s arrears Rs. 80; Rent paid Rs. 1,060; Purchase of cricket balls Rs. 525; Purchase of cricket bats Rs. 580; Miscellaneous expenses Rs. 10; Purchase of Stationery Rs. 5; Salary paid Rs. 1,100.
Solution:
Receipts and Payments A/c for the year ended 31st December, 2001

Question 3.
Subscription received by the Health Club during the year 2014 were as under:

Calculate the amount of Subscription to be shown on the income side of Income and Expenditure A/c.
Solution:
Calculation of Subscription for 2014

Question 4.
During the year 2014, subscription received by a sports club were ₹ 80,000. These included ^ 3,000 for the year 2013 and 16,000 for the year 2015. On Decembrer 31, 2013 amount of subscription due but not reveived was ₹ 12,000. Calculate the ammount of subscription to be shown in Income and Expenditure Account as income from subscription?
Solution
Calculation of Subscription for 2014

Question 5.
The Receipts and Payments Account of Harimohan Charitable Institution is given:

Prepare the Income and Expenditure Account for the year ended on March 31, 2014 after considering the following:
(i) It was decided to treat 50% of the amount received on account of Legacies and Donations as income.
(ii) Liabilities to be provided for are: Rent’ 800; Salaries ‘ 1200; Advertisement’ 200
(iii) ‘2,000 due for interest on investment was not actually received.
Solution:
Income & Expenditure A/c the year ended 31.03.2018

Question 6.
From the following receipts and payments and information given below, prepare Income and Expenditure Account and opening Balance Sheet of Adult Literacy orgnization as on December 31, 2013: Receipts and Payments Account for the year ending as on December31,2013.


Information:
(i) Subscription outstanding as on 31.12.2012, ₹ 2,000 and for the year ending December 31,2013, ₹ 1,500
(ii) On December 31,2013 Salary outstanding’ 600, and one month Rent paid in advance.
(iii) On Jan. 01,2012 organization owned Furniture ₹ 12,000, Books ₹ 5,000.
Solution:

Question 7.
The following is the account of cash transactions of the Nari Kalayan Samittee for the year ended December 31, 2013:

You are required to prepare an Income and Expenditure Account after the following adjustments:
(i) Subscription still to be received are ‘ 750, but subscription include ‘ 500 for the year 2014.
(ii) In the beginning of the year the Sangh owned building ‘ 20,000 and furniture ‘ 3,000 and Books ‘2,000.
(iii) Provide depreciation of furniture @5% (including purchase), books @10% and building @5%.

Tamilnadu State Board New Syllabus Samacheer Kalvi 11th Maths Guide Pdf Chapter 11 Integral Calculus Ex 11.12 Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 11 Integral Calculus Ex 11.12

Integrate the following with respect to x.

Question 1.
(i) \(\sqrt{x^{2}+2 x+10}\)
Answer:

(ii) \(\sqrt{x^{2}-2 x-3}\)
Answer:

(iii) \(\sqrt{(6-x)(x-4)}\)
Answer:

Question 2.
(i) \(\sqrt{9-(2 x+5)^{2}}\)
Answer:

(ii) \(\sqrt{81+(2 x+1)^{2}}\)
Answer:

(iii) \(\sqrt{(x+1)^{2}-4}\)
Answer: