NCERT Solutions for Class 7 Maths Chapter 8
NCERT Solutions for Class 7 Maths Chapter 8:
The purpose of NCERT Solutions for Class 7 Maths Chapter 8 is to assist students in using the formulas to compare quantities and compute ratios to address a variety of situations. Students will learn about ratio and proportion in NCERT Solutions for Class 7 Maths Chapter 8, Comparing Quantities. Additionally, they will learn about the unitary method, percentage, and simple interest ideas and how to use them in real-world situations. This chapter also covers the conversion of decimals and fractions into percentages and vice versa.
NCERT Solutions for Class 7 Maths Chapter 8 PDF
NCERT Solutions
for Class 7 Maths Chapter 8 Comparing Quantities download the attached PDF. Students must practise maths concepts appropriately for each topic if they hope to achieve higher maths scores. You can get higher grades by using the NCERT Solutions for Class 7 Maths Chapter 8. Experts have fix problems step-by-step and provide clear explanations.
NCERT Solutions for Class 7 Maths Chapter 8 PDF
NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities
Below we have provided NCERT Solutions for Class 7 Maths Chapter 8 for students to help them understand the chapter better and to score good marks in their examination.
Exercise 8.1 Page: 157
1. Find the ratio of:
(a) ₹ 5 to 50 paise
Solution:-
We know that,
₹ 1 = 100 paise
Then,
₹ 5 = 5 × 100 = 500 paise
Now we have to find the ratio,
= 500/50
= 10/1
So, the required ratio is 10: 1.
(b) 15 kg to 210 g
Solution:-
We know that,
1 kg = 1000 g
Then,
15 kg = 15 × 1000 = 15000 g
Now we have to find the ratio,
= 15000/210
= 1500/21
= 500/7 … [∵divide both by 3]
So, the required ratio is 500: 7.
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(c) 9 m to 27 cm
Solution:-
We know that,
1 m = 100 cm
Then,
9 m = 9 × 100 = 900 cm
Now we have to find the ratio,
= 900/27
= 100/3 … [∵divide both by 9]
So, the required ratio is 100: 3.
(d) 30 days to 36 hours
Solution:-
We know that,
1 day = 24 hours
Then,
30 days = 30 × 24 = 720 hours
Now we have to find the ratio,
= 720/36
= 20/1 … [∵divide both by 36]
So, the required ratio is 20: 1.
2. In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?
Solution:-
From the question it is given that,
Number of computer required for 6 students = 3
So, number of computer required for 1 student = (3/6)
= ½
So, number of computer required for 24 students = 24 × ½
= 24/2
= 12
∴ Number of computers required for 24 students is 12.
3. Population of Rajasthan = 570 lakhs and population of UP = 1660 lakhs.
Area of Rajasthan = 3 lakh km
2
and area of UP = 2 lakh km
2
.
(i) How many people are there per km
2
in both these states?
(ii) Which state is less populated?
Solution:-
(i)
From the question, it is given that,
Population of Rajasthan = 570 lakh
Area of Rajasthan = 3 lakh Km
2
Then, population of Rajasthan in 1 km
2
area = (570 lakh)/ (3 lakh km
2
)
= 190 people per km
2
Population of UP = 1660 Lakh
Area of UP = 2 Lakh km
2
Then, population of UP in 1 lakh km
2
area = (1660 lakh)/ (2 lakh km
2
)
= 830 people per km
2
(ii)
By comparing the two states, we find that Rajasthan is the less populated state.
Exercise 8.2 Page: 164
1. Convert the given fractional numbers to percent.
(a) 1/8
Solution:-
In order to convert a fraction into a percentage multiply the fraction by 100 and put the percent sign %.
= (1/8) × 100 %
= 100/8 %
= 12.5%
(b) 5/4
Solution:-
In order to convert a fraction into a percentage multiply the fraction by 100 and put the percent sign %.
= (5/4) × 100 %
= 500/4 %
= 125%
(c) 3/40
Solution:-
In order to convert a fraction into a percentage multiply the fraction by 100 and put the percent sign %.
= (3/40) × 100 %
= 300/40 %
= 30/4 %
= 7.5%
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(d) 2/7
Solution:-
In order to convert a fraction into a percentage multiply the fraction by 100 and put the percent sign %.
= (2/7) × 100 %
= 200/7 %
=
%
2. Convert the given decimal fraction to percent.
(a) 0.65
Solution:-
First we have to remove the decimal point,
= 65/100
Now,
Multiply by 100 and put the percent sign %.
We have,
= (65/100) × 100
= 65%
(b) 2.1
Solution:-
First we have to remove the decimal point,
= 21/10
Now,
Multiply by 100 and put the percent sign %.
We have,
= (21/10) × 100
=210%
(c) 0.02
Solution:-
First we have to remove the decimal point,
= 2/100
Now,
Multiply by 100 and put the percent sign %.
We have,
= (2/100) × 100
= 2%
(d) 12.35
Solution:-
First we have to remove the decimal point,
= 1235/100
Now,
Multiply by 100 and put the percent sign %.
We have,
= (1235/100) × 100)
= 1235%
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3. Estimate what part of the figures is coloured, and hence find the per cent which is coloured.
(i)
Solution:-
By observing the given figure,
We can identify that 1 part is shaded out of 4 equal parts.
It is represented by a fraction = ¼
Then,
= ¼ × 100
= 100/4
= 25%
Hence, 25% of the figure is coloured.
(ii)
Solution:-
By observing the given figure,
We can identify that 3 parts are shaded out of 5 equal parts.
It is represented by a fraction = 3/5
Then,
= (3/5) × 100
= 300/5
= 60%
Hence, 60% of the figure is coloured.
(iii)
Solution:-
By observing the given figure,
We can identify that 3 parts are shaded out of 8 equal parts.
It is represented by a fraction = 3/8
Then,
= (3/8) × 100
= 300/8
= 37.5%
Hence, 37.5% of the figure is coloured.
4. Find:
(a) 15% of 250
Solution:-
We have,
= (15/100) × 250
= (15/10) × 25
= (15/2) × 5
= (75/2)
= 37.5
(b) 1% of 1 hour
Solution:-
We know that, 1 hour = 60 minutes
Then,
1% of 60 minutes
1 minute = 60 seconds
60 minutes = 60 × 60 = 3600 seconds
Now,
1% of 3600 seconds
= (1/100) × 3600
= 1 × 36
= 36 seconds
(c) 20% of ₹ 2500
Solution:-
We have,
= (20/100) × 2500
= 20 × 25
= ₹ 500
(d) 75% of 1 kg
Solution:-
We know that, 1 kg = 1000 g
Then,
75% of 1000 g
= (75/100) × 1000
= 75 × 10
= 750 g
5. Find the whole quantity if
(a) 5% of it is 600
Solution:-
Let us assume the whole quantity be x,
Then,
(5/100) × (x) = 600
X = 600 × (100/5)
X = 60000/5
X = 12000
(b) 12% of it is ₹ 1080.
Solution:-
Let us assume the whole quantity is x,
Then,
(12/100) × (x) = 1080
X = 1080 × (100/12)
X = 540 × (100/6)
X = 90 × 100
X = ₹ 9000
(c) 40% of it is 500k km
Solution:-
Let us assume the whole quantity is x,
Then,
(40/100) × (x) = 500
X = 500 × (100/40)
X = 500 × (10/4)
X = 500 × 2.5
X = 1250 km
(d) 70% of it is 14 minutes
Solution:-
Let us assume the whole quantity is x,
Then,
(70/100) × (x) = 14
X = 14 × (100/70)
X = 14 × (10/7)
X = 20 minutes
(e) 8% of it is 40 liters
Solution:-
Let us assume the whole quantity is x,
Then,
(8/100) × (x) = 40
X = 40 × (100/8)
X = 40 × (100/8)
X = 40 × 12.5
X = 500 liters
6. Convert given percent to decimal fractions and also fractions in simplest forms:
(a) 25%
Solution:-
First convert the given percentage into fraction and then put the fraction into decimal form.
= (25/100)
= ¼
= 0.25
(b) 150%
Solution:-
First convert the given percentage into fraction and then put the fraction into decimal form.
= (150/100)
= 3/2
= 1.5
(c) 20%
Solution:-
First convert the given percentage into fraction and then put the fraction into decimal form.
= (20/100)
= 1/5
= 0.2
(d) 5%
Solution:-
First convert the given percentage into fraction and then put the fraction into decimal form.
= (5/100)
= 1/20
= 0.05
7. In a city, 30% are females, 40% are males and remaining are children. What per cent are children?
Solution:-
From the question, it is given that
Percentage of female in a city =30%
Percentage of male in a city = 40%
Total percentage of both male and female = 40% + 30%
= 70%
Now we have to find the percentage of children = 100 – 70
= 30%
So, 30% are children.
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:-
From the question, it is given that
Total number of voters in the constituency = 15000
Percentage of people who voted in the election = 60%
Percentage of people who did not vote in the election = 100 – 60
= 40%
Total number of voters who did not vote in the election = 40% of 15000
= (40/100) × 15000
= 0.4 × 15000
= 6000 voters
∴ 6000 voters did not vote.
9. Meeta saves ₹ 4000 from her salary. If this is 10% of her salary. What is her salary?
Solution:-
Let us assume Meeta’s salary be ₹ x,
Then,
10% of ₹ x = ₹ 4000
(10/100) × (x) = 4000
X = 4000 × (100/10)
X = 4000 × 10
X = ₹ 40000
∴ Meeta’s salary is ₹ 40000.
10. A local cricket team played 20 matches in one season. It won 25% of them. How many matches did they win?
Solution:-
From the question, it is given that
Total matches played by a local team = 20
Percentage of matches won by the local team = 25%
Then,
Number of matches won by the team = 25% of 20
= (25/100) × 20
= 25/5
= 5 matches.
∴ The local team won 5 matches out of 20 matches.
