NCERT Solutions Class 7 Math Chapter – 7 Comparing Quantities Example

Example 1. Write 1/3 as per cent.

Solution – We have, 1/3 = 1/3 x 100/100 = 1/3 x 100%
= 100/3% = 33 x 1/3%

Example 2. Out of 25 children in a class, 15 are girls. What is the percentage of girls?

Solution – Out of 25 children, there are 15 girls.
Therefore, percentage of girls = 15/25 x 100 = 60. There are 60% girls in the class.

Example 3. Convert 5/4 to per cent.

Solution – We have, 5/4 = 5/4 x100% = 125%

From these examples, we find that the percentages related to proper fractions are less than 100 whereas percentages related to improper fractions are more than 100.

Example 4. Convert the given decimals to per cents:

(a) 0.75
(b) 0.09
(c) 0.2

Solution –

(a) 0.75 = 0.75 x 100%
= 75/100 x 100% = 75%

(b) 0.09 = 9/100 = 9%

(c) 0.2 = 2/10 x 100% = 20%

Example 5. What per cent of the adjoining figure is shaded?

Solution – We first find the fraction of the figure that is shaded. From this fraction, the percentage of the shaded part can be found.

You will find that half of the figure is shaded. And, 1/2 = 1/2 x 100% = 50% Thus, 50% of the figure is shaded.

Example 6. A survey of 40 children showed that 25% liked playing football. How many children liked playing football?

Solution – Here, the total number of children are 40. Out of these, 25% like playing football. Meena and Arun used the following methods to find the number. You can choose either method.

Example 7. Rahul bought a sweater and saved ₹200 when a discount of 25% was given. What was the price of the sweater before the discount?

Solution – Rahul has saved ₹200 when price of sweater is reduced by 25%. This means that 25% reduction in price is the amount saved by Rahul. Let us see how Mohan and Abdul have found the original cost of the sweater.

Example 8. Reena’s mother said, to make idlis, you must take two parts rice and one part urad dal. What percentage of such a mixture would be rice and what percentage would be urad dal?

Solution – In terms of ratio we would write this as Rice: Urad dal = 2:1.
Now, 2 + 1 = 3 is the total of all parts. This means 2/3 part is rice and 1/3 part is urad dal.

Then, percentage of rice would be 2/3 x 100% = 200/3 = 66 x 2/3%

Percentage of urad dal would be 1/3 x 100% = 100/3 = 33 x 1/3%

Example 9. If 250 is to be divided amongst Ravi, Raju and Roy, so that Ravi gets two parts, Raju three parts and Roy five parts. How much money will each get? What will it be in percentages?

Solution – The parts which the three boys are getting can be written in terms of ratios as 2:3:5. Total of the parts is 2+3+5=10.

Example 10. A school team won 6 games this year against 4 games won last year. What is the per cent increase?

Solution – The increase in the number of wins (or amount of change) = 6 – 4 = 2.

Percentage increase = amount of change/original amount or base x 100

= increase in the number of wins/original number of wins x 100 = 2/4 x 100 = 50

Example 11. The number of illiterate persons in a country decreased from 150 lakhs to 100 lakhs in 10 years. What is the percentage of decrease?

Solution – Original amount = the number of illiterate persons initially = 150 lakhs.

Amount of change = decrease in the number of illiterate persons = 150 – 100= 50 lakhs
Therefore, the percentage of decrease
amount of change/original amount x 100 = 50/150 x 100 = 33 x 1/3

Example 12. The cost of a flower vase is ₹120. If the shopkeeper sells it at a loss of 10%, find the price at which it is sold.

Solution – We are given that CP= 120 and Loss per cent = 10. We have to find
the SP.

Thus, by both methods we get the SP as ₹108.

Example 13. Selling price of a toy car is ₹540. If the profit made by shopkeeper is20%, what is the cost price of this toy?

Solution – We are given that SP=540 and the Profit=20%. We need to find the CP.

Thus, by both methods, the cost price is ₹450.

Example 14. Anita takes a loan of ₹ 5,000 at 15% per year as rate of interest. Find the interest she has to pay at the end of one year.

Solution – The sum borrowed = 5,000, Rate of interest = 15% per year. This means if 100 is borrowed, she has to pay ₹15 as interest for one year. If she has borrowed 5,000, then the interest she has to pay for one year

= ₹ 15 /100 x 5000 = ₹750

So, at the end of the year she has to give an amount of ₹5,000 + ₹750 = ₹5,750. We can write a general relation to find interest for one year. Take P as the principal or sum and R % as Rate per cent per annum.

Now on every 100 borrowed, the interest paid is ₹ R

Therefore, on ₹ P borrowed, the interest paid for one year would be R x P/100 = P x R /100

Example 15. If Manohar pays an interest of ₹750 for 2 years on a sum of ₹4,500, find the rate of interest.