# NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.2

These NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.2 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities Exercise 8.2

Question 1.
A man got a 10% increase in his salary. If his new salary is ₹ 1,54,000, find his original salary.
Solution:
Let the original salary of a man be ₹ x.
Increase in salary = 10% = $$\frac{10}{100}$$ × x = $$\frac{x}{10}$$
New salary = ₹ 1,54,000
x + $$\frac{x}{10}$$ = 154000
$$\frac{10 x+x}{10}$$ = 154000
11x = 154000 × 10
x = $$\frac{154000 \times 10}{11}$$ = ₹ 1,40,000
∴ Original salary = ₹ 1,40,000

Question 2.
On Sunday 845 people went to the zoo. On Monday only 169 people went. What is the per cent decrease in the people visiting the zoo on Monday?
Solution:
Decrease Value = 845 – 169 = 676
Decrease % = $$\frac{\text { Decrease Value }}{\text { Original Value }} \times 100$$
= $$\frac{676}{845}$$ × 100 = 80%
Decrease % = 80%

Question 3.
A shopkeeper buys 80 articles for ₹ 2400 and sells them for a profit of 16%. Find the selling price of one article.
Solution:
Cost price of 80 articles = ₹ 2400
Profit = $$\frac{16}{100}$$ × 2400 = ₹ 384
Selling price of 80 articles = ₹ 2400 + 384 = ₹ 2784
Selling price of one article = ₹ $$\frac{2784}{80}$$ = ₹ 34.80

Question 4.
The cost of an article was ₹ 15,500. ₹ 450 were spent on its repairs. If it is sold for a profit of 15%, find the selling price of the article.
Solution:
Total cost price of the article = ₹ 15,500 + ₹ 450 = ₹ 15,950
Profit = 15% of C.P.
= $$\frac{15}{100}$$ × 15950
= ₹ 2392.50
Selling Price of the article = ₹ 15950 + ₹ 2392.50 = ₹ 18342.50
∴ S.P of the article = ₹ 18342.50

Question 5.
A VCR and TV were bought for ₹ 8000 each. The shopkeeper made a loss of 4% on the VCR and a profit of 8% on the T. V. Find the gain or loss per cent on the whole transaction.
Solution:
Total C.P. of VCR and T.V. = ₹ 2 × 8000 = ₹ 16000
Loss on VCR = $$\frac{4}{100}$$ × 8000 = ₹ 320
Selling price of the VCR = ₹ 8000 – 320 = ₹ 7680
Profit on T.V. = $$\frac{8}{100}$$ × 8000 = ₹ 640
Selling price of the T.V. = ₹ 8000 + ₹ 640 = ₹ 8640
Total selling price = ₹ 7680 + ₹ 8640 = ₹ 16,320
Combined Profit = ₹ 16320 – ₹ 16000 = ₹ 320
Gain % = $$\frac{\text { Gain }}{\text { Total C.P. }} \times 100$$
= $$\frac{320}{16000}$$ × 100
= 2%
Profit % on the whole = 2%

Question 6.
During a sale, a shop offered a discount of 10% on the marked prices of all the items. What would a customer have to pay for a pair of jeans marked at ₹ 1450 and two shirts marked at ₹ 850 each?
Solution:
Marked price of a pairs of jeans = ₹ 1450
Discount = 10% of M.P
= $$\frac{10}{100}$$ × 1450
= ₹ 145
Sale price of a pair of jeans = ₹ 1450 – ₹ 145 = ₹ 1305
Marked price of two shirts = ₹ 850 × 2 = ₹ 1700
Discount = 10% of M.P
= $$\frac{10}{100}$$ × 1700
= ₹ 170
Sale price of two shirts = ₹ 1700 – 170 = ₹ 1530
∴ Total amount paid by the customer = ₹ 1305 + ₹ 1530 = ₹ 2835
Amount paid by the customer = ₹ 2835

Question 7.
A milkman sold two of his buffaloes for ₹ 20,000 each. On one he made a gain of 5% and on the other a loss of 10%. Find his overall gain or loss. (Find CP of each)
Solution:
Selling price of 1st buffalo = ₹ 20,000
gain% = 5%
Cost price = $$\left(\frac{100}{100+\text { Profit } \%}\right) \times \mathrm{S} . \mathrm{P}$$

Total selling price = ₹ 2 × 20,000 = ₹ 40,000
Loss = Total C.P. – Total S.P
= ₹ 41269.84 – ₹ 40,000
= ₹ 1269.84

Question 8.
The price of a TV is ₹ 13,000. The sales tax charged on it is at the rate of 12%. Find the amount that Vinod will have to pay if he buys it.
Solution:
Cost price of the T.V. = ₹ 13,000
Sales tax = 12% of C.P
= $$\frac{12}{100}$$ × 13000
= ₹ 1560
Bill amount = ₹ 1560 + ₹ 13,000 = ₹ 14,560
∴ Vinod has to pay ₹ 14,560 to buy a TV.

Question 9.
Arun bought a pair of skates at a sale where the discount given was 20%. If the amount he pays is ₹ 1,600. Find the marked price.
Solution:
Let the marked price be ₹ ‘x’
Discount = 20% of M.P
= $$\frac{20}{100}$$ × x
= $$\frac{\mathrm{x}}{5}$$
Amount paid by Arun = ₹ 1600
x – $$\frac{\mathrm{x}}{5}$$ = 1600
$$\frac{5 x-x}{5}=1600$$
x = $$\frac{1600 \times 5}{4}$$ = ₹ 2000
∴ Amount paid by Arun = ₹ 2,000

Question 10.
I purchased a hair-dryer for ₹ 5400 including 8% VAT. Find the price before VAT was added.
Solution:
Let the original price of a hair-dryer be ‘x’
VAT = 8% of original price = $$\frac{8}{100}$$ × x = $$\frac{2 \mathrm{x}}{25}$$
Bill amount = ₹ 5400
x + $$\frac{2 \mathrm{x}}{25}$$ = 5400
$$\frac{25 x+2 x}{25}$$ = 5400
$$\frac{27 \mathrm{x}}{25}$$ = 5400
x = $$\frac{5400 \times 25}{27}$$ = ₹ 5000
∴ Original price of the hair dryer = ₹ 5000

Question 11.
An article was purchased for ₹ 1239 including GST of 18%. Find the price of the article before GST was added?
Solution:
Cost with GST included = ₹ 1239
Cost with out GST = x rupees
GST = 18%
If we take this into equation
x + ((18 ÷ 100 ) × x) = 1239
Cost before GST + GST = Cost with GST
⇒ x + ( 9x ÷ 50 ) = 1239
⇒ (50x + 9x) ÷ 50 = 1239
⇒ 59x ÷ 50 = 1239
⇒ 59x = 1239 × 50
⇒ 59x = 61950
⇒ x = 61950 ÷ 59
⇒ x = 1050
Price before GST = ₹ 1050

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