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\(\frac { 4 }{ 7 }\)%
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:
Question 3.
Estimate what part of the figures is coloured and hence find the per cent which is coloured.
i)
Solution:
\(\frac { 1 }{ 4 }\)th part is coloured
\(\frac { 1 }{ 4 }\) × 100 = 25% is coloured.
ii)
Solution:
\(\frac { 3 }{ 5 }\)th Part is coloured
\(\frac { 3 }{ 5 }\) × 100 = 3 × 20 = 60% is coloured
iii)
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
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.