NCERT Class 7 Maths Chapter 7 Comparing Quantities Exercise 7.1, 7.2 Solutions
In this page we have provided solutions of the Exercises 7.1, 7.2 of NCERT Class 7 Maths Chapter 7 Comparing Quantities. These solutions are made by our team of expert teachers. Practice these solutions carefully for a better understanding of the topic which will help in scoring good marks in the examination.
Publishing Organisation |
NCERT |
Class |
7 |
Subject |
Mathematics |
Chapter |
7: Comparing Quantities |
Exercise |
7.1, 7.2 |
Chapter – 7
Comparing Quantities
Exercise – 7.1
(1) Convert the given fractional numbers to per cents.
(a) 1/8
Ans:- 1/8 × 100/100
= 1/8 × 100%
= 12.5%
(b) 5/4
Ans:- 5/4 × 100/100
= 500/4 %
= 125%
(c) 3/40
Ans:- 3/40 × 100/100
= 300/40%
= 7.5%
(2) Convert the given decimal fractions to per cents.
(a) 0.65
Ans:- 65/100 = 65/100 × 100%
(b) 2.1
Ans:- 21/10 = 21/10 × 100% = 210%
(c) 0.02
Ans:- 2/100 = 2/100 × 100% = 2%
(d) 12.35
Ans:- 1235/100 = 1235/100 × 100% = 1235%
(3) Estimate what part of the figures is coloured and hence find the per cent which is coloured.
Ans:- (i) Here, 1 part out of 4 equal parts are shaded which represents the fraction 1/4.
1/4 = 1/4 × 100% = 25%
(ii) Here, 3 parts out of 5 equal parts are shaded which represents the fraction 3/5.
3/5 = 3/5 × 100% = 60%
(iii) Here, 3 parts out of 8 equal parts are shaded which represents the fraction 3/8.
3/8 = 3/8 × 100% = 300/8% = 37.5%
(4) Find:
(a) 15% 250
Ans:- 15/100 × 250
= 75/2
= 37.5
(b) 1% of 1 hour = 1/100 × 1 hour
Ans:- 1/100 hour
= 60/100 Minute
= 3/5 minute
= 3/5 × 60 Seconds
= 36 Seconds
(c) 20% of Rs. 2500
Ans:- R.S. 20/100 × 2500
R.S = 500
(d) 75% of 1 kg = 75/100 × 1 kg
Ans:- 75/100 × 1 Kg
= 3/4 Kg
= 750 kg.
(5) Find the whole quantity if.
(a) 5% of it is 600.
Ans:- 5/100 × x = 600
X = 600 × 100/5
= 12000
(b) 12% of it is ₹ 1080.
Ans:- 12% of x = R.s = 1080
12/100 × x = R.s 1080
12/100 × x = R.s = 1080
X = Rs 1080 × 100/10 = Rs 9000
(c) 40% of it is 500 km.
Ans:- 40/100 × x =500km
X = 500 × 100/40 = 1250 km
(d) 70% of it is 14 minutes.
Ans:- x × 70/100 = 14 minutes
X = 14 × 100/70 = 20 minutes
(e) 8% of it is 40 litters.
Ans:- 8% of x = 40 L
X × 8/100 = 40 L
X = 40 × 100/8
= 500 L
(6) Convert given per cents to decimal fractions and also to fractions in simplest forms:
(a) 25%
Ans:- 25/100 = 0.25 = 5/20 = 1/4
(b) 150%
Ans:- 150/100 = 1.50 = 3/2
(c) 20%
Ans:- 20/100 = 0.20 = 1/5
(d) 5%
Ans:- 5/100 = 0.05 = 1/20
(7) In a city, 30% are females, 40% are males and remaining are children. What per cent are children?
Ans:- It is given that 30% are females and 40% are males. Children = (100 – 30 – 40)% = 30%
(8) Out of 15,000 voters in a constituency, 60% voted. Find the percentage of voters who did not vote. Can you now find how many actually did not vote?
Ans:- 100% – 60% = 40% did not vote number of voters who did not actually vote = 40% of 15,000
= 40/100 × 15000
= 6000.
(9) Meeta saves ₹ 4000 from her salary. If this is 10% of her salary. What is her salary?
Ans:- Let Meeta’s Salary be RS x.
Given that,
10% of x = 400
10/100 × x = 400
x/10 = 400
x = 400 × 10 = Rs. 4000
Therefore, Meeta’s Salary is Rs 4000.
(10) A local cricket team played 20 matches in one season. It won 25% of them. How many matches did they win?
Ans:- Let the total number of matches won be P. Then,
25% of 20 = P
⇒ 25/100 ×2 20 = P ⇒ 5 = P
⇒ P = 5
Hence, they won 5 matches.
Exercise – 7.2
(1) Tell what is the profit or loss in the following transactions. Also find profit per cent or loss per cent in each case.
(a) Gardening shears bought for ₹ 250 and sold for ₹325.
Ans:- Cost Price = Rs 250
Selling price = Rs 325
Profit = 325 – 250 = Rs 75
Profit % = Profit/CP × 100
= 75/250 × 100
= 30%
(b) A refrigerator bought for ₹ 12,000 and sold at ₹ 13,500.
Ans:- Cost Price = Rs 12000
Selling price = Rs 13, 500
Profit = 13500 – 12000 = Rs 1500
Profit % = Profit/CP × 100
Profit % = 15000/12000 × 100
= 12.5%
(c) A cupboard bought for ₹ 2,500 and sold at ₹ 3,000.
Ans:- Cost Price = Rs 2500
Selling Price = Rs 3000
Profit = 3000 – 2500 = Rs 500
Profit % = Profit/CP × 100
Profit% = 500/2500 × 100
= 20%
(d) A skirt bought for ₹ 250 and sold at ₹ 150.
Ans:- Cost Price = Rs 250
Selling Price = Rs 150
Loss = 250 – 150 = Rs 100
Loss% = Loss/CP × 100
Loss% = 100/250 × 100
= 40%
(2) Convert each part of the ratio to percentage:
(a) 3:1
Ans:- Total of Parts = 3 +1 = 4
First part of the ratio = 3/4 × 100% = 75%
Second Part of the ratio = 1/4 × 100% = 25%
(b) 2:3:5
Ans:- Total of Parts = 2+3+5 = 10
First part of the ratio = 2/5 × 100% = 20%
Second Part of the ratio = 3/10 × 100% = 30%
Third Part of the ratio = 5/10 × 100% = 50%
(c) 1:4
Ans:- Total of Parts = 1+4 = 5
First part of the ratio
= 1/5 × 100 = 20%
Second Part of the ratio = 4/5 × 100 = 80%
(d) 1:2:5
Ans:- Total of Parts = 1 + 2 + 5 = 8
First Part of the ratio
= 1/8 × 100% = 25% or 12.5%
Second Part of the ratio
2/8 × 100% = 25%
Third Part of the ratio
5/8 × 100% = 125/2% or 62.5%
(3) The population of a city decreased from 25,000 to 24,500. Find the percentage decrease.
Ans:- Initial Population = 25000
Final Population = 24500
Decrease = 500
% Decrease = 500/25000 × 100 = 2%
(4) Arun bought a car for ₹ 3, 50, 000. The next year, the price went up to ₹ 3, 70, 000. What was the Percentage of price increase?
Ans:- Percentage increase
= Amount in increase/Original amount × 100%
= 3, 70, 000 – 3, 50, 000/3, 50, 000 × 100%
= 20, 000/3, 50, 000 × 10%
= 40/7% or 5 (5/7) %
(5) I buy a T.V. for ₹ 10, 000 and sell it at a profit of 20%. How much money do I get for it?
Ans:- C.P. = RS. 10, 000
Profit = 20% of C.P
= 20% of Rs 10, 000
= Rs 20/100 × 10, 000 = Rs 2000
∴ S.P. = C.P. + Profit
= Rs 10, 000 + Rs 2,000 = Rs 12, 000
Hence, I get Rs 12, 000 Profit.
(6) Juhi sells a washing machine for ₹ 13, 500. She loses 20% in the bargain. What was the price at which she bought it?
Ans:- Selling Price = Rs 13500
Loss% = 20%
Let the cost price be x.
∴ Loss = 20% of x
Cost Price – Loss = Selling Price
X – 20/100 × X = 13500
X – 1/5 × = 13500
4/5 × = 13500
X = 13500 × 5/4
= 16875
Therefore, she bought it for Rs 16875.
(7) (i) Chalk contains calcium, carbon and oxygen in the ratio 10:3:12. Find the percentage of carbon in chalk.
Ans:- Total of Parts = 10+3+12 = 25
Percentage of Carbon in Chalk
= 3/25 × 100% = 12%
(ii) If in a stick of chalk, carbon is 3g, what is the weight of the chalk stick?
Ans:- Let the weight of the chalk stick of chalk be P. Then, 12% of P = 3
⇒ 12/100 × P = 3
⇒ P = 3 × 100/12 = 25 g
⇒ P = 25 g
Hence, the weight of the chalk stick is 25 g.
(8) Anima buys a book for ₹ 275 and sells it at a loss of 15%. How much does she sell it for?
Ans:- Cost Price = Rs 275
Loss% = 15%
Loss = 15% 275
Cost Price – Loss = Selling Price
275 – 15/100 × 275 = Selling Price
275 – 4125/100 = Selling Price
275 – 41.25 = Selling Price
Selling Price = RS 233.75
(9) Find the amount to be paid at the end of 3 years in each case:
(a) Principal = ₹ 1,200 at 12% p.a.
Ans:- P = Rs 1,200,
R = 12% p.a.
T = 3 Years
I = PRT/100
= 1,200 × 12 × 3/100 = Rs 432
A = P + I
= 1200 + 432
= Rs 1,632
Hence, the amount to the paid at end of 3 years is Rs 1632.
(b) Principal = ₹ 7,500 at 5% p.a.
Ans:- P = Rs 7, 500. R = 5% p.a.
T = 3 years
I = PRT/100
= 7,500 × 5 × 3/100
= Rs. 1125
A = P + I
⇒ A = 7, 500 + 1,125
= Rs. 8625
Hence, the amount to be paid at the end of 3 years is Rs 8,625.
(10) What rate gives ₹ 280 as interest on a sum of ₹ 56, 000 in 2 years?
Ans:- S.I = P × R × T/100
280 = 56000 × R × 2/100
R = 280/560 × 2 = 1/4 = 0.25
Therefore, 0.25% gives Rs 280 is in interest on the given sum.
(11) If Meena gives an interest of ₹45 for one year at 9% rate p.a.. What is the sum she has borrowed?
Ans:- I = Rs 45, R = 9% p.a.
Let the sum be Rs P.
I = PR/100
⇒ 45 = P × q/100
⇒ P = 45 × 100/9
= 500
Hence, the Sum she has borrowed is Rs 500.
Chapter 6: The Triangles And Its Properties