**NCERT Solutions for Class 8 Maths Chapter 8 Exercise 8.2 – Comparing Quantities, has been designed by the NCERT to test the knowledge of the student on the following topics:-**

- Finding the Increase or Decrease Per cent
- Finding Discounts

Estimation in percentages - Prices Related to Buying and Selling (Profit and Loss)

Finding cost price/selling price, profit %/loss% - Sales Tax/Value Added Tax/Goods and Services Tax

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

**NCERT Solutions for Class 8 Maths Chapter 8 Exercise 8.2 – Comparing Quantities**

**Q.1 A man got a 10% increase in his salary. If his new salary is Rs 1,54,000, find his original salary. **

**Solution:**

Given, new salary is Rs 1,54,000.

Let, the original salary be ‘x’

10% increment in salary = (10/100) × x

New salary = Original salary + Increase in salary

154000 = x + (10/100) × x

x + (10/100) × x = 154000

x = 140000

Therefore, original salary is Rs. 1,40,000

**Q.2 On Sunday 845 people went to the Zoo. On Monday only 169 people went. What is the percent decrease in the people visiting the Zoo on Monday? **

**Solution**:

Given, on Sunday 845 people went to the zoo and on Monday only 169 people went.

Decrease in the number of people went to Zoo = 845 − 169 = 676

Percentage decrease = (676/845) x 100% = 80%

Therefore, percentage decrease in the people visiting the Zoo on Monday is 80%

**Q.3 A shopkeeper buys 80 articles for Rs 2,400 and sells them for a profit of 16%. Find the selling price of one article. **

**Solution: **

Given, A shopkeeper buys 80 articles for Rs 2,400 and sells them for a profit of 16%

Cost of one article = (2400/80) = Rs. 30

We know that profit percentage = (Profit/Cost Price) × 100

16 x (Profit/30) x 100

Profit = Rs. 4.80

Selling price = Cost price + Profit = 30 + 4.80 = Rs. 34.80

Therefore, the selling price of one article is Rs. 34.80

**Q.4 The cost of an article was Rs 15,500. Rs 450 were spent on its repairs. If it is sold for** **a profit of 15%, find the selling price of the article. **

**Solution:**

Given,

The cost of an article was Rs 15,500.

Rs 450 were spent on its repairs and sold for a profit of 15%

Total Cost Price of article = 15,500 + 450 = Rs. 15950

Profit percent = 15%

(Profit/Cost Price) x 100 = 15

(Profit/15950) x 100 = 15

Profit = (15950 × 15)/100

Profit = Rs. 2392.50

Therefore, Selling price of the article = Cost Price + Profit = 15950 + 2392.50

= Rs. 18342.50

**Q.5 A VCR and TV were bought for Rs 8,000 each. The shopkeeper made a loss of 4% on the VCR and a profit of 8% on the TV. Find the gain or loss percent on the whole transaction. **

**Solution: **

Given, Cost Price of a VCR = Rs. 8000

The shopkeeper made a loss of 4% on VCR.

Loss = (Cost Price/100) × Loss percent

Loss = (8000/100) × 4

Loss = Rs. 320

Therefore, selling price of VCR is 8000 – 320 = Rs. 7680

Given, Cost Price of a TV = Rs 8000

The shopkeeper made a profit of 8 % on TV.

Profit = (Cost Price/100) × profit percent

Profit = (8000/100) × 8

Profit = Rs. 640

Therefore, Selling price of TV = 8000 + 640 = Rs. 8640

Total Cost Price = 8000 + 8000 = Rs. 16000

Total Selling Price = 7680 + 8640 = Rs. 16320

Selling Price > Cost Price => Profit

Therefore, Profit = 16320 − 16000 = Rs. 320

Profit Percentage = (16320 – 16000)/16000 x 100 = 2%

Therefore, the gain percent on whole transaction is 2%

**Q.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 Rs 1450 and two shirts marked at Rs. 850 each? **

**Solution: **

Given, during a sale, a shop offered a discount of 10% on marked prices of all items

Total marked price pair of jeans marked at Rs 1450 and two shirts marked at Rs. 850

each = 1450 + 2 × 850 = Rs. 3150

Discount percent = 10%

Discount = (10/100) x 3150 = Rs. 315

Selling Price = Cost Price – discount

Selling Price = 3150 – 315 = Rs. 2835

Therefore, the customer would have to pay Rs 2835

**Q.7 A milkman sold two of his buffaloes for Rs 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. (Hint: Find CP of each)**

**Solution:**

Given, A milkman sold two of his buffaloes for Rs 20,000 each

Gain percent on one buffalo is 5% and loss percent on another is 10%

First buffalo is sold at a gain of 5%

Cost Price of one buffalo = 20000 x (100/105) = 19047.62

Therefore, Cost Price of first buffalo = Rs. 19,047.62

Second buffalo was sold at a loss of 10%

Cost Price of second buffalo = 20000 x (100/90) = 22222.22

Therefore, Cost Price of second buffalo = Rs. 22222.22

Total Cost Price = 19047.62 + 22222.22 = Rs. 41269.84

Total Selling Price = 20000 + 20000 = Rs. 40000

Selling Price < Cost Price => Loss

Loss = 41269.84 − 40000 = Rs. 1269.84

Therefore, overall loss of Milkman is Rs. 1269.84.

**Q.8 The price of a TV is Rs 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:**

Given, the price of a TV is Rs 13,000 and sales tax charged on it is at the rate of 12%

12% tax on Rs. 13000 = 13000 x (12/100) = 1560

Amount of Tax on to be paid = Rs. 1560

Amount to be paid = Cost + Sales Tax = 13000 + 1560 = Rs. 14560

Therefore, the amount Vinod will have to pay is Rs 14,560

**Q.9 Arun bought a pair of skates at a sale where the discount given was 20%. If the amount he pays is Rs. 1,600, find the marked price. **

**Solution:**

Given, Arun bought a pair of skates at a sale where the discount given was 20%

Amount paid by Arun is Rs. 1600

Let, the marked price be ‘x’

Discount = Marked price − Sale price

Discount percent = (Discount/Marked Price) × 100

20 = (Discount/x) × 100

Discount = (x/5)

(x/5) = x – 1600 [ Discount = Marked price − Sale price ]

1600 = x – (x/5)

1600 = (4x/5)

x = 2000

Therefore, the marked price is Rs. 2000

**Q.10 I purchased a hair-dryer for Rs. 5,400 including 8% VAT. Find the price before VAT as added. **

**Solution:**

Given, I purchased a hair-dryer for Rs. 5,400 including 8% VAT

Let, ‘x’ be the initial price

x + x × (18/100) = 5400

(118x/100) = 5400

x = 5400 x (100/118)

x = 5000

Therefore, the price of the hair-dryer before VAT was added is Rs. 5,000.

**Q.11 An article was purchased for Rs. 1239 including GST of 18%. Find the price of the ****article before GST was added?**

**Solution:**

Given, an article was purchased for Rs. 1239 including GST of 18%

Let, ‘x’ be the initial price

x + x × (18/100) =1239

(118x/100) = 1239

x = 1239 x (100/118)

x = 1050

Therefore, Price of the article before GST was added is Rs. 1050

**The next Exercise for** **NCERT Solutions for Class 8 Maths Chapter 8 Exercise 8.3 – Comparing Quantities can be accessed by clicking here**

**Download NCERT Solutions for Class 8 Maths Chapter 8 Exercise 8.2 – Comparing Quantities**

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