AP 7th Class Maths 7th Chapter Comparing Quantities Exercise 7.1 Solutions

Well-designed AP 7th Class Maths Guide Chapter 7 Comparing Quantities Exercise 7.1 offers step-by-step explanations to help students understand problem-solving strategies.

Lines and Angles Class 7 Exercise 7.1 Solutions – 7th Class Maths 7.1 Exercise Solutions

Question 1.
Convert the given fractional numbers to percents.
a) \(\frac { 1 }{ 8 }\)
Solution:
\(\frac { 1 }{ 8 }\) = \(\frac { 1 }{ 8 }\) × 100 = \(\frac { 50 }{ 4 }\) = \(\frac { 25 }{ 2 }\) = 12\(\frac { 1 }{ 2 }\)% = 12.5%

b) \(\frac { 5 }{ 4 }\)
Solution:
\(\frac { 5 }{ 4 }\) = \(\frac { 5 }{ 4 }\) × 100 = 5 × 25 = 125%

c) \(\frac { 3 }{ 40 }\)
Solution:
\(\frac { 3 }{ 40 }\) = \(\frac { 3 }{ 40 }\) × 100 = \(\frac { 30 }{ 4 }\) = \(\frac { 15 }{ 2 }\) = 7\(\frac { 1 }{ 2 }\)% = 7.5%

d) \(\frac { 2 }{ 7 }\)
Solution:
\(\frac { 2 }{ 7 }\) = \(\frac { 2 }{ 7 }\) × 100 = \(\frac { 200 }{ 7 }\) = 28\(\frac { 4 }{ 7 }\)%

AP 7th Class Maths 7th Chapter Comparing Quantities Exercise 7.1 Solutions

Question 2.
2. Convert the given decimal fractions to per cents.
a) 0.65
Solution:
0.65 = \(\frac { 65 }{ 100 }\) = 65%

b) 2.1
Solution:
2.1 = \(\frac{\frac{21}{10}}{100}\) = \(\frac{21 \times 100}{10}\) = 210%

c) 0.02
Solution:
0.02 = \(\frac{\frac{2}{100}}{100}\) = \(\frac{2 \times 100}{100}\) = 2%

b) 12.35
Solution:
AP 7th Class Maths 7th Chapter Comparing Quantities Exercise 7.1 Solutions Img 1

Question 3.
Estimate what part of the figures is coloured and hence find the per cent which is coloured.
i) AP 7th Class Maths 7th Chapter Comparing Quantities Exercise 7.1 Solutions Img 2
Solution:
\(\frac { 1 }{ 4 }\)th part is coloured
\(\frac { 1 }{ 4 }\) × 100 = 25% is coloured.

ii) AP 7th Class Maths 7th Chapter Comparing Quantities Exercise 7.1 Solutions Img 3
Solution:
\(\frac { 3 }{ 5 }\)th Part is coloured
\(\frac { 3 }{ 5 }\) × 100 = 3 × 20 = 60% is coloured

iii) AP 7th Class Maths 7th Chapter Comparing Quantities Exercise 7.1 Solutions Img 4
Solution:
\(\frac { 3 }{ 8 }\)th Part is coloured
\(\frac { 3 }{ 8 }\) × 100 = \(\frac { 300 }{ 8 }\) = \(\frac { 150 }{ 4 }\) = \(\frac { 75 }{ 2 }\) = 37.5% is coloured

Question 4.
Find
a) 15% of 250
Solution:
15% of 250 = \(\frac { 15 }{ 100 }\) × 250 = \(\frac { 15 }{ 10 }\) × 25 = \(\frac { 3 }{ 2 }\) × 25 = \(\frac { 75 }{ 2 }\) = 37.5

b) 1% of 1 hour
Solution:
1% of 1 hour = \(\frac { 1 }{ 100 }\) × 60
= \(\frac{6}{10}\) = \(\frac { 3 }{ 5 }\) minutes = \(\frac { 3 }{ 5 }\) × 60 seconds
= 3 × 12 seconds = 36 seconds

c) 20% of ₹ 2500
Solution:
20% of ₹ 2500 = \(\frac { 20 }{ 100 }\) × 2500 = 20 × 25 = ₹ 500

d) 75% of 1 kg
Solution:
75% of 1 kg = \(\frac { 75 }{ 100 }\) × 1000 g
= \(\frac { 3 }{ 4 }\) × 1000 g = 3 × 250 g = 750 g = 0.75 kg

AP 7th Class Maths 7th Chapter Comparing Quantities Exercise 7.1 Solutions

Question 5.
Find the whole quantity if
a) 5% of it is 600.
Solution:
Let the whole quantity be x.
5 % of x = 600
\(\frac{5}{100}\) × x = 600
\(\frac{x}{20}\) = 600 ⇒ x = 600 × 20 = 12000
∴ 5% of 12000 is 600

b) 12% of it is ₹ 1080
Solution:
12% of x = ₹ 1080
\(\frac{12}{100}\) × x = 1080
\(\frac{6}{50}\) × x = 1080
\(\frac{3}{25}\) × x = 1080
x = 1080 × \(\frac{25}{3}\)
x = 360 × 25 ⇒ x = ₹ 9000
∴ 12% of ₹ 9000 = ₹ 1080

c) 40% of it is 500 km.
Solution:
40% of x = 500 km
\(\frac{40}{100}\) × x = 500
\(\frac{4}{10}\) × x = 500
\(\frac{2}{5}\) × x = 500
x = 500 × \(\frac{5}{2}\)
x = 250 × 5 ⇒ x = 1250 km
∴ 40% of 1250 km = 500 km

d) 70% of it is 14 minutes.
Solution:
70% of x = 14 minutes
\(\frac{70}{100}\) × x = 14
\(\frac{7}{10}\) × x = 14
x = 14 × \(\frac{10}{7}\) ⇒ x = 2 × 10 ⇒ x = 20 minutes
∴ 70% of 20 minutes = 14 minutes

e) 8% of it is 40 litres.
Solution:
8% of x = 40 litres
\(\frac{8}{100}\) × x = 40
\(\frac{4}{50}\) × x = 40
\(\frac{2}{25}\) × x = 40
x = 40 × \(\frac{25}{2}\)
x = 20 × 25 ⇒ x = 500 litres
∴ 8% of 500 litres = 40 litres.

Question 6.
Convert given per cents to decimal fractions and also to fractions in simplest forms :
a) 25%
Solution:
25% = \(\frac{25}{100}\) = \(\frac{1}{4}\) = 0.25

b)150%
Solution:
150% = \(\frac{150}{100}\) = \(\frac{15}{10}\) = \(\frac{3}{2}\) = 1.5

c) 20%
Solution:
20% = \(\frac{20}{100}\) = \(\frac{2}{10}\) = \(\frac{1}{5}\) = 0.2

d) 5%
Solution:
5% = \(\frac{5}{100}\) = \(\frac{1}{20}\) = 0.05

Question 7.
In a city, 30% are females, 40% are males and remaining are children. What per cent are children?
Solution:
In a city, % of females = 30%
% of males = 40%
Remaining % = 100% – 30% – 40% = 100% – 70% = 30%
∴ 30% are children.

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:
Number of voters in constituency = 15,000
% of voted = 60%
% of voters who did not vote = 100% – 60% = 40%
40% of 15,000
= \(\frac { 40 }{ 100 }\) × 15,000 = = \(\frac { 4 }{ 10 }\) × 15,000 = 4 × 1500 = 6000
∴ 6000 voters did not vote.

Question 9.
Meeta saves ₹4000 from her salary. If this is 10% of her salary. What is her salary?
Solution:
Meeta’s saving from salary = ₹ 4000
% of savings = 10%
10% – 4000; 100% – ?
? = \(\frac{100 \times 4000}{10}\) = ₹ 40,000
∴ Meeta’s salary =₹ 40,000

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 cricket matches a team played = 20
1 % of won = 25%
25% of 20 = \(\frac { 25 }{ 10 }\) × 20 = \(\frac { 1 }{ 4 }\) × 20 = 5
∴ 5 matches won by the team.

Leave a Comment