Tamilnadu State Board New Syllabus Samacheer Kalvi 8th Maths Guide Pdf Chapter 4 Life Mathematics Ex 4.4 Text Book Back Questions and Answers, Notes.
Tamilnadu Samacheer Kalvi 8th Maths Solutions Chapter 4 Life Mathematics Ex 4.2
Question 1.
Fill in the blanks:
(i) Loss or gain percentage is always calculated on the ________ .
Answer:
Cost Price
(ii) A mobile phone is sold for ₹ 8400 at a gain of 20%. The cost price of the mobile phone is ________ .
Answer:
₹ 7000
Hint:
Let cost price of mobile be ₹ x
Given that selling price is ₹ 8400 and gain is 20%
As per formula,
(iii) An article is sold for ₹ 555 at a loss of 7\(\frac { 1 }{ 2 }\)%. The cost price of the article is ________ .
Answer:
₹ 600
Hint:
Given selling price is ₹ 555 & loss 7\(\frac { 1 }{ 2 }\)%
as per formula
(iv) A mixer grinder marked at ₹ 4500 is sold for ₹ 4140 after discount. The rate of discount is ________ .
Answer:
8 %
Hint:
Marked price is ₹ 4500
Discounted price in ₹ 4140
∴ Discount = Marked price – Discounted priòe
= 4500 – 4140 = 360
(v) The total bill amount of a shirt costing ₹ 575 and a T-shirt costing ₹ 325 with GST of 5% is ________ .
Answer:
Cost of price shirt = ₹ 575 (CP)
GST = 5%
Cost of price shirt = ₹ 325 (CP)
GST = 5%
∴ Total bill amount = ₹ 603.75 + ₹ 341.25 = ₹ 945
Question 2.
If selling an article for ₹ 820 causes 10% loss on the selling price, then find its cost price.
Answer:
Given that selling price (SP) = ₹ 820
Loss % = 10 %
Question 3.
If the profit earned on selling an article for ₹ 810 is the same as loss on selling it for ₹ 530, then find the cost price of the article.
Answer:
Case 1: Profit = Selling price (SP) – Cost price (CP)
Case 2: Loss = Cost price (CP) – Selling price (SP)
Given that profit of case 1 = loss of case 2
∴ P = 810 – CP
L = CP – 530
Since profit (P) = loss (L)
810 – CP = CP – 530
∴ 2CP = 810 + 530 = 1340 ⇒ C.P = \(\frac{1340}{2}\)
∴ CP = 670
Question 4.
If the selling price of 10 rulers is the same as the cost price of 15 rulers, then find the profit percentage.
Answer:
Let cost price of one ruler be x
Given that selling price (SP) of 10 rulers.
i.e., same as cost price (CP) of 15 rulers
∴ SP of 10 rulers = 15 × x = 15x
∴ SP of 1 ruler = \(\frac{15 x}{10}\) = 1.5x
∴ Gain = SP of 1 ruler – CP of 1 ruler = 1.5x – x = 0.5x
Question 5.
Some articles are bought at 2 for ₹ 15 and sold at 3 for ₹ 25. Find the gain percentage.
Answer:
Let cost price of one article be C.P
Given that 2 are bought for ₹ 15
∴ 2 × CP = 15 ⇒ CP = \(\frac{15}{2}\)
Let selling price of one article be SP
Given that 3 are sold for ₹ 25
∴ 3 × SP = 25 ⇒ SP = \(\frac{25}{3}\)
∴ Gain = SP – CP = \(\frac{25}{3}-\frac{15}{2}=\frac{50-45}{6}=\frac{5}{6}\)
= \(11 \frac{1}{9}\)
Question 6.
By selling a speaker for ₹ 768, a man loses 20%. In order to gain 20%, how much should he sell the speaker?
Answer:
Selling price (SP) of speaker = ₹ 768
Loss % = 20 %
as per formula
∴ CP = \(\frac{768 \times 100}{80}\) = 960
For gain of 20%, we should now calculate the selling price
= 96 × 12 = ₹ 1152
Question 7.
Find the unknowns x, y and z.
Answer:
(i) Book marked price = ₹ 225 discount 8%
∴ Selling price (x) = Marked price × \(\left(\frac{(100-d \%)}{100}\right)\)
= 225 × \(\frac{(100-8)}{100}\) = 225 × \(\frac{92}{100}\) = ₹ 207
(ii) LED TV selling price = 11970 discount = 5%, Marked price = y
∴ Selling price Marked price y × \(\left(\frac{(100-d \%)}{100}\right)\)
∴ 11970 = y × \(\frac{(100-5)}{100}\)
∴ y = \(\frac{11970 \times 100}{95}\) = 126 × 100 = ₹ 12,600
(iii) Digital clock marked price (MP) = ₹ 750, MP = ₹ 12.600
Selling price (SP) = ₹ 615, Discount = z
100 – z = 82
∴ z = 100 – 82, Discount = 18%
Question 8.
Find the total bill amount for the data given below:
Answer:
Formula for discounted price LW = Marked price (MP) × \(\frac{(100-d \%)}{100}\)
When d is the discount %
For bill amount, we should apply GST on the discounted value of the items.
Formula: Bill amount = Discounted price × \(\left(\frac{(100+\mathrm{GST} \%)}{100}\right)\)
∴ For (i) School bag.
Bill amount 475 × \(\left(\frac{(100+12)}{100}\right)\) = 475 × 1.12 = %‘532
∴ For (ii) Hair drier,
Bill amount = 1800 × \(\left(\frac{(100+28)}{100}\right)\) = 1800 × 1.28 =
∴ Total bill amount Bill amount of School bag + Stationary + Cosmetics + Hair drier
= 532 + 252 + 1357 + 2304
= ₹ 4.445
Question 9.
A branded Air-Conditioner (AC) has a marked price of ₹ 38000. There are 2 options given for the customer.
(i) Selling Price is the same ₹ 38000 but with attractive gifts worth ₹ 3000
(or)
(ii) Discount of 8% on the marked price but no free gifts. Which offer is better?
Answer:
Marked price of AC = ₹ 38,000
Option 1:
Selling price = ₹ 38000 & gifts worth ₹ 3000
∴ Net gain for customer = ₹ 3000 as there is no discount on AC
Option 2:
Discount of 8%, but no gift
∴ Discounted value = MP × \(\left(\frac{(100-d \%)}{100}\right)\)
38000 × \(\frac{(100-8)}{100}\) = 38000 × 0.92 = 34960
∴ Savings for customer = 38000 – 34960 = 3040
Therefore, the customer gets 3000 gift in option I where as he is able to save only ₹ 3040 in option 2. Therefore, option 2 is better.
Question 10.
If a mattress is marked for ₹ 7500 and is available at two successive discount of 10% and 20%, find the amount to be paid by the customer.
Answer:
Marked price of mattress = ₹ 7500
Discount d1 = 10%
Discount d2 = 20%
Objective Type Questions
Question 11.
A fruit vendor sells fruits for ₹ 200 gaining ₹ 40. His gain percentage is
(A) 20%
(B) 22%
(C) 25%
(D) 16
Answer:
(C) 25%
Hint:
Selling price ₹ 200
Gain = 40
∴ CP – Selling price – gain = 200 – 40 = 160
Question 12.
By selling a flower pot for Z528, a woman gains 20%. At what price should she sell it to gain 25%?
(A) ₹ 500
(B) ₹ 550
(C) ₹ 553
(D) ₹ 573
Answer:
(B) ₹ 550
Hint:
If selling price (sp) = ₹ 528
Gain % = 20 %
∴ CP = ?
Question 13.
A man buys an article for ₹ 150 and makes overhead expenses which are 12% of the cost price. At what price must he sell it to gain 5%?
(A) ₹ 180
(B) ₹ 168
(C) ₹ 176.40
(D) ₹ 88.20
Answer:
(C) ₹ 176.40
Hint:
Cost price of article = ₹ 150
Over head expenses = 12% of cost price
= \(\frac{12}{100}\) × 150 = ₹ 18
∴ Effective cost of article = 150 + 18 = ₹ 168
Now, to gain 5%, he has to sell at
Question 14.
What is the marked price of a hat which is bought for Z210 at 16% discount?
(A) ₹ 243
(B) ₹ 176
(C) ₹ 230
(D) ₹ 250
Answer:
(D) ₹ 250
Hint:
Let marked price be MP
Discounted price = ₹ 210
Rate of discount = 16%
As per formula:
Question 15.
The single discount in % which is equivalent to two successive discounts of 20% and 25% is
(A) 40%
(B) 45%
(C) 5%
(D) 22.5%
Answer:
(A) 40%
Hint:
Let marked price be MP, after discount 1 of 20%,
Comparing with formula, we get
∴ This is equivalent to a single discount of 40%