Comparing Quantities
(Percentage)
Important Points
1. Per cent is derived from Latin word ‘per centum’ meaning ‘per or out of hundred’
2. 25% = 25 out of hundred = 25/100 = 1/4 = 0.25
3. Graphically it can be represented as shown.
4.Fractions and decimals can be converted to percentages and vice versa.
Q1: Convert the following to per cents:
Answer:
NCERT Exercise 8.2
Q1: Convert the given fractional numbers to per cents.
(a) 1/8 (b) 5/4 (c) 3/40 (d) 2/7
Answer:
(a) 1/8 = 1 × 100 / 8 = 12.5%
(b) 5/4 = 5 × 100/4 = 125%
(c) 3/40 = 3 × 100/40 = 30/4 = 7.25%
Q2: Convert the given decimal fractions to per cents.
(a) 0.65 (b) 2.1 (c) 0.02 (d) 12.35
Answer:
Q3: Estimate what part of the figures is coloured and hence find the per cent which is coloured.
Answer:
(i) Total Parts = 4
Filled part = 1
Filled part in fraction = 1/4
% of Filled part = (1/4) × 100 = 100/4 = 25%
(ii) Total Parts = 5
Filled parts = 3
Filled parts in fraction = 3 out of 5 = 3/5
Filled parts in percent = (3/5) × 100 = 3 × 20 = 60%
(iii) Total parts = 8
Filled parts = 3
Filled parts in fraction = 3/8
Filled parts in percent = (3/8) × 100 = 3 × 12.5 = 37.5%
Q4: Find: (a) 15% of 250 (b) 1% of 1 hour (c) 20% of Rs 2500 (d) 75% of 1 kg
Answer:
(a) 15% of 250
= (15/100) of 250 = (15/100) × 250
= 15 × 25/10 = 375/10 = 37.5
(b) 1% of 1 hour
= (1/100) of 1 hour
= (1/100) × 3600 seconds (∵ 1 hour = 3600 seconds)
= 36 seconds
(c) 20% of Rs 2500
= (20/100) of 2500
= (20/100) × 2500
= 20 × 25 = Rs 500
(d) 75% of 1 kg
= (75/100) of 1 kg
= (75/100) × 1
= 0.75 kg
(∵ 1 kg = 1000 grams)
= 0.75 × 1000g = 750g
Q5: Find the whole quantity if
(a) 5% of it is 600. (b) 12% of it is Rs 1080. (c) 40% of it is 500 km.
(d) 70% of it is 14 minutes. (e) 8% of it is 40 litres.
Answer:
(a) 5% of it is 600.
⇒ 5% of n = 600
⇒ (5/100) of n = 600
⇒ (5/100) × n = 600
⇒ n = 600 × (100/5) = 600 × 20 = 12000
(b) 12% of it is Rs 1080.
⇒ 12% of n = 1080
⇒ (12/100) of n = 1080
⇒ (12/100) × n = 1080
⇒ n = 1080 × (100/12) = 90 × 100 = ₹ 9000
(c) 40% of it is 500 km
⇒ 40% of y = 500
⇒ (40/100) of y = 500
⇒ (4/10) × y = 500
⇒ y = 500 × (10/4) = 125 × 10 = 1250 km
(d) 70% of it is 14 minutes.
⇒ 70% of t = 14 mins
⇒ (70/100) of t = 14
⇒ (7/10) × t = 14
⇒ t = 14 × (10/7) = 2 × 10 = 20 minutes
(e) 8% of it is 40 litres
⇒ 8% of n = 40
⇒ (8/100) of n = 40
⇒ (8/100) × n = 40
⇒ n = 40 × (100/8) = 5 × 100 = 500 litres
Q6: Convert given per cents to decimal fractions and also to fractions in simplest forms:
(a) 25% (b) 150% (c) 20% (d) 5%
Answer:
(a) 25% = 25/100 = 0.25
= 25/100 = 1/4
(b) 150% = 150/100 = 15/10 = 3/2 = 1.5
(c) 20% = 20/100 = 2/10 = 1/5 = 0.20
(d) 5% = 5/100 = 1/20 = 0.05
Q7: In a city, 30% are females, 40% are males and remaining are children. What per cent are children?
Answer: Number of females in city = 30%
Number of males in city = 40%
Number of children in city = x%
∴ Females % + Males % + Children % = 100% (Total population of city)
∴ 30% + 40% + x% = 100%
∴ 70% + x% = 100%
∴ x% = 100 - 70 = 30%
∴ Children are 30% of the total population.
Q8: 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?
Answer: Let the total voters = 100%
Voters who voted in % = 60%
⇒ Percentage of voters who did not vote = 100 - 60 = 40%
Total Voters = 15000
⇒ 40% of 15000 did not vote = 40% of 15000
= (40/100) of 15000
= (4/10) × 1500
= 4 ×150 = 6000
Thus 40% voters i.e. 6000 did not vote.
Q9: Meeta saves Rs 400 from her salary. If this is 10% of her salary. What is her salary?
Answer: Let Meeta's salary = ₹ n
Given, she saves 10% of her salary = ₹ 400
⇒ 10% of n = 400
⇒ (10/100) of n = 400
⇒ (1/10) × n = 400
⇒ n = 400 × (10/1) = 4000
Thus Meeta's salary is ₹4000
Q10: A local cricket team played 20 matches in one season. It won 25% of them. How many matches did they win?
Answer: Total matches played = 20
Winning % = 25%
⇒ Matches won = 25% of 20
= (25/100) of 20
= (1/4) × 20 = 5
Thus local cricket team won 5 matches.
Miscellaneous Questions
Q11: In a school having strength of 740 students, 35% study French. How many do not learn French.
Answer: Total number of students = 740
Number of students learn French = 35%
∴ Number of students who do not study French = 100 - 35 = 65%
∴ Actual number of students not studying French = 65% of 740
= 65% of 740
= (65/100) of 740
= (13/20) × 740
= 13 × 37
= 481
Thus 481 students do not study French.
Q12: Decrease 300 by 24%
Answer: Decrease 300 by 24%
∴ New value is = (100 -24)% of 300
= 76% of 300
= (76/100) of 300
= (76/100) × 300
= 76 × 3
= 228
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