Comparing Quantities - Solutions 2

CBSE Class –VII Mathematics
NCERT Solutions
Chapter 8 Comparing Quantities (Ex. 8.2)

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Question 1. Convert the given fractional numbers to percent:

(a) 18$\frac{1}{8}$

(b) 54$\frac{5}{4}$

(c) 340$\frac{3}{40}$

(d) 27$\frac{2}{7}$

Answer: (a) 18$\frac{1}{8}$ = 18×100%=252%$\frac{1}{8}\times 100\mathrm{\%}=\frac{25}{2}\mathrm{\%}$ = 12.5%

(b) 54$\frac{5}{4}$ = 54×100%=$\frac{5}{4}\times 100\mathrm{\%}=$ 5 x 25% = 125%

(c) 340$\frac{3}{40}$ = 340×100%=32×5%=152%$\frac{3}{40}\times 100\mathrm{\%}=\frac{3}{2}\times 5\mathrm{\%}=\frac{15}{2}\mathrm{\%}$ = 7.5%

(d) 27=27×100%=2007%=2847%$\frac{2}{7}=\frac{2}{7}\times 100\mathrm{\%}=\frac{200}{7}\mathrm{\%}=28\frac{4}{7}\mathrm{\%}$

Question 2. Convert the given decimal fractions to percents:

(a) 0.65

(b) 2.1

(c) 0.02

(d) 12.35

Answer: (a) 0.65 = 65100×100%$\frac{65}{100}\times 100\mathrm{\%}$ = 65%

(b) 2.1 = 2110×100%$\frac{21}{10}\times 100\mathrm{\%}$ = 210%

(c) 0.02 = 2100×100%$\frac{2}{100}\times 100\mathrm{\%}$ = 2%

(d) 12.35 = 1235100×100%$\frac{1235}{100}\times 100\mathrm{\%}$= 1235%

Question 3. Estimate what part of the figures is coloured and hence find the percent which is coloured:

Answer: (i) Coloured part = 14$\frac{1}{4}$

∴$\therefore$ Percent of coloured part = 14×100%$\frac{1}{4}\times 100\mathrm{\%}$ = 25%

(ii) Coloured part = 35$\frac{3}{5}$

∴$\therefore$ Percent of coloured part = 35×100%$\frac{3}{5}\times 100\mathrm{\%}$ = 60%

(iii) Coloured part = 38$\frac{3}{8}$

∴$\therefore$ Percent of coloured part = 38×100%$\frac{3}{8}\times 100\mathrm{\%}$ = 32×25%$\frac{3}{2}\times 25\mathrm{\%}$

= 37.5%

Question 4. 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 = 15100×250$\frac{15}{100}\times 250$ = 15 x 2.5 = 37.5

(b) 1% of 1 hours = 1% of 60 minutes = 1% of (60 x 60) seconds

= 1100×60×60$\frac{1}{100}\times 60\times 60$ = 6 x 6 = 36 seconds

(c) 20% of Rs. 2500 = 20100×2500$\frac{20}{100}\times 2500$ = 20 x 25 = Rs. 500

(d) 75% of 1 kg = 75% of 1000 g = 75100×1000$\frac{75}{100}\times 1000$ = 750 g = 0.750 kg

Question 5. 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 liters

Answer: Let the whole quantity be x$x$ in given questions:

(a) 5% of x$x$ = 600

⇒$\Rightarrow$ 5100×x=600$\frac{5}{100}\times x=600$

⇒$\Rightarrow$ x=600×1005$x=\frac{600\times 100}{5}$ = 12,000

(b) 12% of x$x$ = Rs. 1080

⇒$\Rightarrow$12100×x=1080$\frac{12}{100}\times x=1080$

⇒$\Rightarrow$ x=1080×10012$x=\frac{1080\times 100}{12}$ = Rs. 9,000

(c) 40% of x$x$ = 500 km

⇒$\Rightarrow$ 40100×x=500$\frac{40}{100}\times x=500$

⇒$\Rightarrow$ x=500×10040$x=\frac{500\times 100}{40}$ = 1,250 km

(d) 70% of x$x$ = 14 minutes

⇒$\Rightarrow$ 70100×x=14$\frac{70}{100}\times x=14$

⇒$\Rightarrow$ x=14×10070$x=\frac{14\times 100}{70}$ = 20 minutes

(e) 8% of x$x$ = 40 liters

⇒$\Rightarrow$ 8100×x=40$\frac{8}{100}\times x=40$

⇒$\Rightarrow$ x=40×1008$x=\frac{40\times 100}{8}$ = 500 liters

Question 6. Convert given percents to decimal fractions and also to fractions in simplest forms:

(a) 25%

(b) 150%

(c) 20%

(d) 5%

Answer:

S. No.	Percents	Fractions	Simplest form	Decimal form
(a)	25%	25100$\frac{25}{100}$	14$\frac{1}{4}$	0.25
(b)	150%	150100$\frac{150}{100}$	32$\frac{3}{2}$	1.5
(c)	20%	20100$\frac{20}{100}$	15$\frac{1}{5}$	0.2
(d)	5%	5100$\frac{5}{100}$	120$\frac{1}{20}$	0.05

Question 7. In a city, 30% are females, 40% are males and remaining are children. What percent are children?

Answer: Given: Percentage of females = 30%

Percentage of males = 40%

Total percentage of females and males = 30 + 40 = 70%

Percentage of children = Total percentage – Percentage of males and females

= 100% – 70%

= 30%

Hence, 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?

Answer: Total voters = 15,000

Percentage of voted candidates = 60%

Percentage of not voted candidates = 100% – 60% = 40%

Actual candidates, who did not vote = 40% of 15000 = 40100×15000$\frac{40}{100}\times 15000$ = 6,000

Hence, 6,000 candidates did not vote.

Question 9. Meeta saves Rs. 400 from her salary. If this is 10% of her salary. What is her salary?

Answer: Let Meera’s salary be Rs.x.$x.$

Now, 10% of salary = Rs. 400

⇒$\Rightarrow$ 10% of x$x$ = Rs. 400

⇒$\Rightarrow$ 10100×x=400$\frac{10}{100}\times x=400$

⇒$\Rightarrow$ x=400×10010$x=\frac{400\times 100}{10}$

⇒$\Rightarrow$ x=$x=$ 4,000

Hence, Meera’s salary is Rs. 4,000.

Question 10. A local cricket team played 20 matches in one season. It won 25% of them. How many matches did they win?

Answer: Number of matches played by cricket team = 20

Percentage of won matches = 25%

Total matches won by them = 25% of 20 = 25100×20$\frac{25}{100}\times 20$ = 5

Hence, they won 5 matches.