Class 8 Maths Ex. 7.2 Comparing Quantities: NCERT Solutions

In the exercise 7.2, we are going to solve questions on “Finding Discounts” and “Sales Tax/Value Added Tax(VAT)/Goods and Services Tax”. Lets have a look at some basics –

Finding Discounts

Discounts are reductions on the original price of an item. For example, if a book costing ₹500 has a discount of 10%, the discount amount is 10% of ₹500 = ₹50. Therefore, the discounted price of the book would be ₹500 – ₹50 = ₹450.

Sales Tax/Value Added Tax (VAT)/Goods and Services Tax (GST)

Sales Tax

If a product costs ₹1000 and the sales tax rate is 12%, the sales tax amount is 12% of ₹1000 = ₹120. Total cost including sales tax: ₹1000 + ₹120 = ₹1120.

Value Added Tax (VAT)

For a product priced at ₹1500 with VAT at 15%, VAT amount is 15% of ₹1500 = ₹225. Total cost including VAT: ₹1500 + ₹225 = ₹1725.

Goods and Services Tax (GST)

For a service costing ₹2000 with a GST rate of 18%, the GST amount is 18% of ₹2000 = ₹360. Total cost including GST: ₹2000 + ₹360 = ₹2360.

NCERT Solutions for Class 8 Maths Exercise 7.2 Chapter 7 Comparing Quantities

1. 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

Given –
Marked price of pair of jeans = ₹ 1450
Marked price of one shirt = ₹ 850

Discount on jeans = 10% of ₹ 1450 = ₹ 145
Sale price of jeans = ₹ 1450 – ₹ 145 = ₹ 1305

Discount on one shirt = 10% of ₹ 850 = ₹ 85
Sale price of one shirt = ₹ 850 – ₹ 85 = ₹ 765

Sale price for two shirts = ₹ 765 × 2 = ₹ 1530

Total amount to pay = Sale price of jeans + Sale price for two shirts = ₹ 1305 + ₹ 1530 = ₹ 2835.

2. The price of a TV is ₹ 13000. 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 –
Price of TV = ₹ 13000
Sales tax rate = 12%

Sales tax on TV = 12% of ₹ 13000 = ₹ (13000 × 0.12) = ₹ 1560
Total amount to pay = Price of TV + Sales tax = ₹ 13000 + ₹ 1560 = ₹ 14560

For buying the TV, Vinod has to pay ₹ 14560

3. Arun bought a pair of skates at a sale where the discount given was 20%. If the amount he pays is ₹ 1600 find the marked price.

Solution

Given –
Sale price after 20% discount = ₹ 1600
Discount rate = 20%

Let the marked price be x.
x – 20% of x = ₹ 1600
x – (0.20x) = ₹ 1600
0.80x = ₹ 1600
x = ₹ 1600 / 0.80 = ₹ 2000

Marked price of the skates = ₹ 2000

Method 2:
If we assume the marked price to be ₹ 100, then after a 20% discount, the sale price would be ₹ 80 (since 20% of ₹ 100 is ₹ 20, and ₹ 100 – ₹ 20 = ₹ 80).

Therefore, a sale price of ₹ 80 corresponds to an actual payment of ₹ 1600.
To find the marked price that corresponds to this actual payment, we use the proportion:

If ₹ 80 = ₹ 1600,
Then, ₹ 1 = ₹ 1600 / 80 = ₹ 20

Therefore, the marked price (which we assumed as ₹ 100) would be:
₹ 100 × ₹ 20 = ₹ 2000

The marked price of the skates is ₹ 2000.

4. I purchased a hair-dryer for ₹ 5400 including 8% VAT. Find the price before VAT was added.

Solution

Given –
Price including 8% VAT = ₹ 5400
VAT rate = 8%

Let the original price be x.
x + 8% of x = ₹ 5400
1.08x = ₹ 5400
x = ₹ 5400 / 1.08 = ₹ 5000

Price before VAT was added = ₹ 5000.

Method 2:
If the original price is considered 100%, then the price including 8% VAT is 108% of the original price. This means ₹ 5400 represents 108% of the original price.

To find the original price (100%), we can set up the equation where 108% corresponds to ₹ 5400. We need to find the value of 100% (the price before VAT).

Let the original price (100%) be x.
108% of x = ₹ 5400
Therefore, 1.08x = ₹ 5400

To find x (the original price before VAT), we calculate:
x = ₹ 5400 / 1.08 = ₹ 5000

Thus, the price before VAT was added = ₹ 5000.

5. An article was purchased for ₹ 1239 including GST of 18%. Find the price of the article before GST was added?

Solution

Given –
Price including 18% GST = ₹ 1239
GST rate = 18%

Let the original price be x.
x + 18% of x = ₹ 1239
1.18x = ₹ 1239
x = ₹ 1239 / 1.18 = ₹ 1050

Price before GST was added = ₹ 1050.

Method 2:
If the original price is considered 100%, then the price including 18% GST is 118% of the original price. This means ₹ 1239 represents 118% of the original price.

To find the original price (100%), we can set up the equation where 118% corresponds to ₹ 1239. We need to find the value of 100% (the price before GST).

Let the original price (100%) be x.
118% of x = ₹ 1239
Therefore, 1.18x = ₹ 1239

To find x (the original price before GST), we calculate:
x = ₹ 1239 / 1.18 = ₹ 1050

Thus, the price before GST was added = ₹ 1050.

Practice Worksheet with Challenging Questions For Class 8 Ex. 7.2 Comparing Quantities

Questions

1. Find the selling price of a shirt originally marked at ₹800, after applying a discount of 12%.
2. A TV is sold at ₹15,000 after a 25% discount. Find its original price.
3. Calculate the compound interest on ₹10,000 for 3 years at an annual interest rate of 5%, compounded annually.
4. The population of a town increases by 10% every year. If the current population is 50,000, what will it be in two years?
5. If the cost of a laptop is ₹45,000 excluding 18% GST, find the total cost including GST.
6. A car depreciates at a rate of 10% per annum. If its current value is ₹200,000, what was its value 2 years ago?
7. Find the final amount after applying a 15% VAT on an item priced at ₹1200.
8. A book is bought for ₹350 after a discount of 30%. Calculate its marked price.
9. Calculate the sale price of a bicycle after a discount of 20% on the marked price of ₹2500.
10. A sum of ₹5000 is invested in a savings account at 6% per annum. Find the interest after 1 year.
11. Find the amount of sales tax on an article costing ₹800 at the rate of 5%.
12. If a commodity’s price increases by 20% annually, find its price after one year, originally priced at ₹1500.
13. Calculate the compound interest on ₹8000 for 2 years at 4% per annum, compounded annually.
14. An item with a marked price of ₹600 is sold at a discount of 10%. Find the sale price.
15. The price of a laptop, including 12% VAT, is ₹28,000. Find the price before VAT.

Answers

1. Selling price of the shirt: ₹704.
2. Original price of the TV: ₹20,000.
3. Compound interest: ₹1576.25.
4. Population after two years: 60,500.
5. Total cost including GST: ₹53,100.
6. Original value of the car: ₹247,933.33 approximately.
7. Final amount including VAT: ₹1380.
8. Marked price of the book: ₹500.
9. Sale price of the bicycle: ₹2000.
10. Interest after 1 year: ₹300.
11. Sales tax amount: ₹40.
12. Price after one year: ₹1800.
13. Compound interest: ₹656.32.
14. Sale price of the item: ₹540.
15. Price before VAT: ₹25,000.