NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities Exercise 8.1
Ex 8.1 Class 7 Maths Question 1.
Find the ratio of:
(a) ₹ 5 to 50 paise
(b) 15 kg to 210 g
(c) 9 m to 27 cm
(d) 30 days to 36 hours
Solution:
(a) ₹ 5 to 50 paise
Converting the given quantities into same units, we have
₹ 5 = 5 × 100 = 500 paise
∴ ₹ 5 : 50 paise
= 500 paise : 50 paise [∵ ₹ 1 = 100 paise]
= 10 : 1
So, required ratio is 10 : 1.

(b) 15 kg to 210 g
Converting the given quantities into same units, we have
15 kg = 15 × 1000
= 15000 g [∵ 1 kg = 1000 g]
∴ 15 kg : 210 g = 15000 g : 210 g
= 1500 : 21
= 500 : 7
So, the required ratio is 500 : 7.

(c) 9 m to 27 cm
Converting the given quantities into same units, we have
9 m = 9 × 100 = 900 cm
∴ 9m: 27 cm = 900 cm : 27 cm [∵ 1 m = 100 cm]
= 100 : 3
So, the required ratio is 100 : 3.

(d) 30 days to 36 hours
Converting the given quantities into same
units, we have
30 days = 30 × 24 hours [ ∵ 1 day = 24 hours]
= 720 hours
∴ 30 days : 36 hours
= 720 hours : 36 hours = 20:1
So, the required ratio is 20 : 1.

Ex 8.1 Class 7 Maths Question 2.
In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?
Solution:
Using Unitary Method, we have
6 students require 3 computers
∴ 1 student will require = 36 computers
∴ 24 students will require = 36 x 24 computers
= 3 × 4 computers = 12 computers
Hence the number of computers required = 12.

Ex 8.1 Class 7 Maths Question 3.
Population of Rajasthan = 570 lakhs and population of UP = 1660 lakhs.
Area of Rajasthan = 3 lakh km2 and area of UP = 2 lakh km2.
(i) How many people are there per km2 in both these States?
(ii) Which State is less populated?
Solution:
Given:
Population of Rajasthan = 570 lakhs
Population of UP = 1660 lakhs
Area of Rajasthan = 3 lakh km²
Area of UP = 2 lakh km²
(i) Number of people per km² of Rajasthan 5
=570 lakhs 3 lakh km2
= 190 per km²
Number of people in UP = 1660 lakhs
Area of UP = 2 lakh km²
Number of people per km² of UP
= =1660 lakhs 2 lakh km2=830 per km2
Since 190 per km²< 830 per km²
(ii) Rajasthan is less populated state.

NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities Exercise 8.2

Ex 8.2 Class 7 Maths Question 1.
Convert the given fractional numbers to per cents:

Solution:

Ex 8.2 Class 7 Maths Question 2.
Convert the given decimal fractions to per cents:
(а) 0.65
(b) 2.1
(c) 0.02
(d) 12.35
Solution:
(a) 0.65 = 0.65×100100 = 0.65 × 100% = 65%
(b) 2.1 = 2.1×100100 = 2.1 ×100% = 210%
(c) 0.02 = 0.02×100100 = 0.02 × 100% = 2%
(d) 12.35 = 12.35×100100 = 12.35 × 100% = 1235%

Ex 8.2 Class 7 Maths Question 3.
Estimate what part of the figures is coloured and hence find the per cent which is coloured.

Solution:
(i) Fraction of coloured part = 14
∴ Percentage of coloured parts 100

(ii) Fraction of coloured part = 36
∴ Percentage of coloured parts

(iii) Fraction of coloured part = 68
∴ Percentage of coloured parts

Ex 8.2 Class 7 Maths Question 4.
Find:
(a) 15% of 250
(b) 1% of 1 hour
(c) 20% of ₹ 2500
(d) 75% of 1 kg
Solution:
(a) 15% of 250 = 15100×250=752=37.5
(b) 1% of 1 hour = 1% of 60 minutes [∵ 1 h = 60 min.]

Ex 8.2 Class 7 Maths Question 5.
Find the whole quantity if
(a) 5% of it is 600
(b) 12% of it is? 1080
(c) 40% of it is 500 km
(d) 70% of it is 14 minutes
(e) 8% of it is 40 litres
Solution:
Let the required whole quantity be x.
(a) 5% of x = 600

Thus the required whole quantity is 12,000.

(b) 12% of x = ₹ 1080

Thus, the required quantity is ₹ 9,000.

(c) 40% of x = 500 km

Thus, the required quantity = 1250 km.

(d) 70% of x = 14 minutes

Thus, the required quantity = 20 minutes,

(e) 8% of x = 40 litre 8

Thus, the required quantity = 500 litres

Ex 8.2 Class 7 Maths Question 6.
Convert given per cents to decimal fractions and also to fractions in simplest forms:
(a) 25%
(b) 150%
(c) 20%
(d) 5%
Solution:

Ex 8.2 Class 7 Maths Question 7.
In a city, 30% are females, 40% are males and remaining are children. What per cent are children?
Solution:
Given: 30% are females
40% are males
Total Percentage of females and males
= 30% + 40% = 70%
∴ Percentage of children
= (100 – 70)% = 30%

Ex 8.2 Class 7 Maths Question 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?
Solution:
Total number of voters = 15,000
Percentage of the voters who voted = 60%
∴ Percentage of the voters who did not vote
= (100 – 60)% = 40%
Actual number of voters who did not vote
= 40% of 15,000
=40100×15,000=6,000

Ex 8.2 Class 7 Maths Question 9.
Meena saves ₹ 400 from her salary. If this is 10% of her salary. What is her salary?
Solution:
Let Meena’s salary by ₹ x.
∴ 10% of x = ₹ 400

Thus, her salary is ₹ 4000.

Ex 8.2 Class 7 Maths Question 10.
A local cricket team played 20 matches in one season. It won 25% of them. How many matches did they win?
Solution:
Number of matches played by the cricket team = 20
Percentage of the matches won by them = 25%
i.e. 25100×20=5 matches
Thus, the number of matches won by them = 5

NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities Exercise 8.3
Ex 8.3 Class 7 Maths Question 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.
(b) A refrigerator bought for ₹ 12,000 and sold at ₹ 13,500.
(c) A cupboard bought for ₹ 2,500 and sold at ₹ 3,000.
(d) A skirt bought for ₹ 250 and sold at ₹ 150.
Solution:
(a) Here, CP = ₹ 250
SP = ₹ 325
Since SP > CP
∴ Profit = SP – CP
= ₹ 325 – ₹ 250 = ₹ 75

Hence, the required profit = ₹ 75
and Profit per cent = 30%

(b) Here, CP = ₹ 12,000
SP = ₹ 13,500
Since SP > CP
∴ Profit = SP – CP
= ₹ 13,500 – ₹ 12,000 = ₹ 1,500

Hence, the required profit = ₹ 1500 × 100
profit % = 1212%

(c) Here, CP = ₹ 2500
SP = ₹ 3000
Since SP > CP
∴ Profit = SP – CP
= ₹ 3000 – ₹ 2500 = ₹ 500

Hence, the required profit = ₹ 500 and profit% = 20%

(d) Here, CP = ₹ 250
SP = ₹ 150
Here CP > SP
∴ Loss = CP – SP
= ₹ 250 – ₹ 150 = ₹ 100

Hence, the required loss = ₹ 100 and loss% = 40%

Ex 8.3 Class 7 Maths Question 2.
Convert each part of the ratio to Percentage:
(a) 3:1
(b) 2:3:5
(c) 1 : 4
(d) 1:2:5
Solution:
(a) 3 : 1
Sum of the ratio parts = 3 + 1 = 4

(b) 2 : 3 : 5
Sum of the ratio parts = 2 + 3 + 5 = 10

(c) 1 : 4
Sum of the ratio parts =1 + 4 = 5

(d) 1 : 2 : 5
Sum of the ratio parts = 1 + 2 + 5 = 8

Ex 8.3 Class 7 Maths Question 3.
The population of a city decreased from 25,000 to 24,500. Find the Percentage decrease.
Solution:
Initial population = 25,000
Decreased population = 24,500
Decrease in population
= 25,000 – 24,500 = 500
Percentage of decrease = 500×10025000 = 2%
Hence the Percentage of decrease in population = 2%.

Ex 8.3 Class 7 Maths Question 4.
Arun bought a car for ₹ 3,50,000. The next year, the price went upto ₹ 3,70,000. What was the Percentage of price increase?
Solution:
Original price of the car = ₹ 3,50,000
Price increased next year = ₹ 3,70,000
Increase in price = ₹ 3,70,000 – ₹ 3,50,000
= ₹ 20,000
∴ Percentage of the increase in the price

Hence, the Percentage of increase in price = 557%

Ex 8.3 Class 7 Maths Question 5.
I buy a TV for ₹ 10,000 and sell it at a profit of 20%. How much money do I get for it?
Solution:
Here, CP = ₹ 10,000
Profit = 20%
SP = ?

Hence, the required money got by me = ₹ 12,000.

Ex 8.3 Class 7 Maths Question 6.
Juhi sells a washing machine for ₹ 13,500. She loses 20% in the bargain. What was the price at which she bought it?
Solution:
SP of the washing machine = ₹ 13,500
Loss = 20%
CP = ?

Hence, the cost price of the machine = ₹ 16875.

Ex 8.3 Class 7 Maths Question 7.
(i) Chalk contains calcium, carbon and oxygen in the ratio 10 : 3 : 12. Find the Percentage of carbon in chalk.
(ii) If in a stick of chalk, carbon is 3 g, what is the weight of the chalk stick?
Solution:
(i) Sum of the ratio parts = 10 + 3 + 12 = 25
∴ Percentage of carbon in chalk
= =325×100%=12%
Hence, the Percentage of carbon in chalk = 12%

(ii) Weight of carbon = 3 g
∴ Weight of chalk = =33 × 25 g = 25 g
Hence, the weight of chalk = 25 g

Ex 8.3 Class 7 Maths Question 8.
Amina buys a book for ₹ 275 and sells it at a loss of 15%. How much does she sell it for?
Solution:
CP of book = ₹ 275
Loss = 15%

Hence, the required selling price = ₹ 233.75

Ex 8.3 Class 7 Maths Question 9.
Find the amount to be paid at the end of 3 years in each case.
(a) Principal = ₹ 1200 at 12% p.a.
(b) Principal = ₹ 7500 at 5% p.a.
Solution:
(a) Given: Principal = ₹ 1200
Rate of interest = 12% p.a., T = 3 years
∴ Interest = P×R×T100=1200×12×3100
Amount = Principal + Interest
= ₹ 1200 + ₹ 432 = ₹ 1632
Hence, the required amount = ₹ 1632

(b) Given: Principal = ₹ 7500
Rate = 5% p.a.
Time = 3 years
∴ Interest = P×R×T100=7500×5×3100
= ₹1125
Amount = Principal + Interest
= ₹ 7500 + 11125 = ₹ 8625
Hence, the required amount = ₹ 8625.

Ex 8.3 Class 7 Maths Question 10.
What rate gives ₹ 280 as interest on a sum of ₹ 56,000 in 2 years?
Solution:
Given: Principal = ₹ 56,000
Interest = ₹280
Time = 2 years
Rate = ?

Hence, the required rate = 0.25%

Ex 8.3 Class 7 Maths Question 11.
If Meena gives an interest of ₹ 45 for one year at 9% rate p.a. What is the sum she has borrowed?
Solution:
Given: Interest = ₹ 45
Time = 1 year
Rate = 9% p.a.

Hence, the required sum = ₹ 500.