**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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