RS Aggarwal 2019,2020 solution class 7 chapter 10 Percentage Exercise 10A

Exercise 10A

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Question 1:

Convert each of the following fraction into a percentage:

(i) $\frac{47}{100}$
(ii)  $\frac{9}{20}$
(iii) $\frac{3}{8}$
(iv) $\frac{8}{125}$
(v) $\frac{19}{500}$
(vi) $\frac{4}{15}$
(vii) $\frac{2}{3}$
(viii) $1\frac{3}{5}$

Answer 1:

We have the following:

(i) $\frac{47}{100}=\left(\frac{47}{100}\times 100\right)\% = 47\%$

(ii) $\frac{9}{20}=\left(\frac{9}{20}\times 100\right)\% =\left(9\times 5\right)\%= 45\%$

(iii) $\frac{3}{8}=\left(\frac{3}{8}\times 100\right)\% =\left(\frac{3\times 25}{2}\right)\%=\left(\frac{75}{2}\right)\%=37\frac{1}{2}\%$

(iv) $\frac{8}{125}=\left(\frac{8}{125}\times 100\right)\%=\left(\frac{8\times 4}{5}\right)\%=\left(\frac{32}{5}\right)\%=6.4\%$

(v) $\frac{19}{500}=\left(\frac{19}{500}\times 100\right)\%=\left(\frac{19}{5}\right)\%=3.8\%$

(vi) $\frac{4}{15}=\left(\frac{4}{15}\times 100\right)\%=\left(\frac{4\times 20}{3}\right)\%=\left(\frac{80}{3}\right)\%=26\frac{2}{3}\%$

(vii) $\frac{2}{3}=\left(\frac{2}{3}\times 100\right)\%=\left(\frac{200}{3}\right)\%=66\frac{2}{3}\%$

(viii) $1\frac{3}{5}=\frac{8}{5}=\left(\frac{8}{5}\times 100\right)\%=(8\times 20)\%=160\%$

Question 2:

Convert each of the following into a fraction:

(i) 32%
(ii) $6\frac{1}{4}\%$
(iii) $26\frac{2}{3}\%$
(iv) 120%
(v) 6.25%
(vi) 0.8%
(vii) 0.06%
(viii) 22.75%

Answer 2:

We have the following:

(i) $32\%=\left(\frac{32}{100}\right)=\frac{8}{25}$

(ii) $6\frac{1}{4}\%=\left(\frac{25}{4}\right)\%=\left(\frac{25}{4}\times \frac{1}{100}\right)=\frac{1}{16}$

(iii) $26\frac{2}{3}\%=\left(\frac{80}{3}\right)\%=\left(\frac{80}{3}\times \frac{1}{100}\right)=\left(\frac{4\times 1}{3\times 5}\right)=\frac{4}{15}$

(iv) $120\%=\left(\frac{120}{100}\right)=\frac{6}{5}=1\frac{1}{5}$

(v) $6.25\%=\left(\frac{6.25}{100}\right)=\left(\frac{625}{100\times 100}\right)=\left(\frac{25}{400}\right)=\frac{1}{16}$

(vi) $0.8\%=\left(\frac{0.8}{100}\right)=\left(\frac{8}{10\times 100}\right)=\left(\frac{8}{1000}\right)=\frac{1}{125}$

(vii) $0.06\%=\left(\frac{0.06}{100}\right)=\left(\frac{6}{100\times 100}\right)=\left(\frac{6}{10000}\right)=\frac{3}{5000}$

(viii)  $22.75\%=\left(\frac{22.75}{100}\right)=\left(\frac{2275}{100\times 100}\right)=\frac{91}{400}$

Question 3:

Express each of the following as a ratio:

(i) 43%
(ii) 36%
(iii) 7.5%
(iv) 125%

Answer 3:

We have:

(i) $43\%=\frac{43}{100}=43 : 100$

(ii) $36\%=\frac{36}{100}=\frac{9}{25}=9 : 25$

(iii) $7.5\%=\left(\frac{7.5}{100}\right)=\left(\frac{75}{10\times 100}\right)=\frac{3}{40}=3 : 40$

(iv) $125\%=\frac{125}{100}=\frac{5}{4}=5 : 4$

Question 4:

Convert each of the following ratios into a percentage:

(i) 37 : 100
(ii) 16 : 25
(iii) 3 : 5
(iv) 5 : 4

Answer 4:

We have the following:

(i) 37 : 100 = $\frac{37}{100}=\left(\frac{37}{100}\times 100\right)\%=37\%$

(ii) 16 : 25 = $\frac{16}{25}=\left(\frac{16}{25}\times 100\right)\%=\left(16\times 4\right)\%=64\%$

(iii) 3 : 5 =$\frac{3}{5}=\left(\frac{3}{5}\times 100\right)\%=\left(3\times 20\right)\%=60\%$

(iv) 5 : 4 = $\frac{5}{4}=\left(\frac{5}{4}\times 100\right)\%=\left(5\times 25\right)\%=125\%$

Question 5:

Convert each of the following into decimal form:

(i) 45%
(ii) 127%
(iii) 3.6%
(iv) 0.23%

Answer 5:

We have the following:

(i) 45% = $\left(\frac{45}{100}\right)=0.45$

(ii) 127% = $\left(\frac{127}{100}\right)=1.27$

(iii) 3.6% =$\left(\frac{3.6}{100}\right)=\left(\frac{36}{10\times 100}\right)=\frac{36}{1000}=0.036$

(iv) 0.23% =$\left(\frac{0.23}{100}\right)=\left(\frac{23}{100\times 100}\right)=\frac{23}{10000}=0.0023$

Question 6:

Convert each of the following decimals into a percentage:

(i) 0.6
(ii) 0.42
(iii) 0.07
(iv) 0.005

Answer 6:

We have:

(i) 0.6 = (0.6 $\times$ 100)% = 60%
(ii) 0.42 = (0.42 $\times$ 100)% = 42%
(iii) 0.07 = (0.07 $\times$ 100)% = 7%
(iv) 0.005 = (0.005 $\times$ 100)% = 0.5%

Question 7:

Find:

(i) 32% of 425
(ii) $16\frac{2}{3}\% \mathrm{of} 16$
(iii) 6.5% of 400
(iv) 136% of 70
(v) 2.8% of 35
(vi) 0.6% of 45

Answer 7:

We have:
 (i) 32% of 425 = $\left(\frac{32}{100}\times 425\right)=\left(\frac{32\times 17}{4}\right)=\left(8\times 17\right)=136$

(ii) $16\frac{2}{3}\%$ of 16 = $\frac{50}{3}\%$ of 16 = $\left(\frac{50}{3\times 100}\times 16\right)=\left(\frac{1}{6}\times 16\right)=\frac{8}{3}=2\frac{2}{3}$

(iii) 6.5% of 400 = $\left(\frac{6.5}{100}\times 400\right)=\left(\frac{65}{10\times 100}\times 400\right)=\left(\frac{65\times 4}{10}\right)=\frac{260}{10}=26$

(iv) 136% of 70 = $\left(\frac{136}{100}\times 70\right)=\left(\frac{136\times 7}{10}\right)=\left(\frac{952}{10}\right)=95.2$

(v) 2.8% of 35 = $\left(\frac{2.8}{100}\times 35\right)=\left(\frac{28}{10\times 100}\times 35\right)=\left(\frac{14\times 7}{100}\right)=\frac{98}{100}=0.98$

(vi) 0.6% of 45  = $\left(\frac{0.6}{100}\times 45\right)=\left(\frac{6}{10\times 100}\times 45\right)=\left(\frac{3\times 45}{5\times 100}\right)=\left(\frac{3\times 9}{100}\right)=\frac{27}{100}=0.27$

Question 8:

Find:

(i) 25% of Rs 76
(ii) 20% of Rs 132
(iii) 7.5% of 600 m
(iv) $3\frac{1}{3}\% \mathrm{of} 90 \mathrm{km}$
(v) 8.5% of 5 kg
(vi) 20% of 12 litres

Answer 8:

We have the following:

(i) 25% of Rs 76 = Rs $\left(76\times \frac{25}{100}\right)$ = Rs $\left(76\times \frac{1}{4}\right)$ = Rs 19

(ii) 20% of Rs 132 = Rs $\left(132\times \frac{20}{100}\right)$= Rs $\left(132\times \frac{1}{5}\right)$ = Rs 26.4

(iii) 7.5% of 600 m = $\left(600\times \frac{7.5}{100}\right) \mathrm{m}=\left(6\times 7.5\right) \mathrm{m}=45 \mathrm{m}$

(iv) $3\frac{1}{3}\%$ of 90 km = $\frac{10}{3}\%$of 90 km =$\left(90\times \frac{10}{3\times 100}\right) \mathrm{km}=\left(90\times \frac{1}{30}\right) \mathrm{km}=3 \mathrm{km}$

(v) 8.5% of 5 kg = $\left(5\times \frac{8.5}{100}\right) \mathrm{kg}=\left(5\times \frac{85}{1000}\right) \mathrm{kg}=0.425 \mathrm{kg}=425 \mathrm{g}$         [∵1 kg = 1000 g]

(vi) 20% of 12 L = $\left(12\times \frac{20}{100}\right) \mathrm{L}=\left(12\times \frac{1}{5}\right) \mathrm{L}=2.4 \mathrm{L}$

Question 9:

Find the number whose 13% is 65.

Answer 9:

Let x be the required number.

Then, 13% of x = 65  
⇒ $\left(\frac{13}{100}\times x\right)=65$
⇒ x = $\left(65\times \frac{100}{13}\right)=500$
Hence, the required number is 500.

Question 10:

Find the number whose $6\frac{1}{4}\%$ is 2.

Answer 10:

Let x be the required number.
Then, $6\frac{1}{4}\%$ of x = 2
⇒ $\left(6\frac{1}{4}\%\times x\right)=2$
⇒ $\left(\frac{25}{400}\times x\right)=2$
⇒  x = $\left(2\times \frac{400}{25}\right)=32$
Hence, the required number is 32.

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Question 11:

What amount is 10% more than Rs 90?

Answer 11:

10% of Rs 90 = Rs $\left(\frac{10}{100}\times 90\right)$ = Rs 9
∴ Amount that is 10% more than Rs 90 = Rs (90 + 9) = Rs 99

Hence, the required amount is Rs 99.

Question 12:

What amount is 20% less than Rs 60?

Answer 12:

20% of Rs 60 = Rs $\left(60\times \frac{20}{100}\right)$= Rs 12
∴ Amount that is 20% less than Rs 60 = Rs (60 − 12) = Rs 48

Hence, the required amount is Rs 48.

Question 13:

If 3% of x is 9, find the value of x.

Answer 13:

3% of x = 9
⇒ $\left(\frac{3}{100}\times x\right)=9$
⇒ x = $\left(9\times \frac{100}{3}\right)=300$
Hence, the value of x is 300.

Question 14:

If 12.5% of x is 6, find the value of x.

Answer 14:

12.5% of x = 6
⇒ $\left(\frac{12.5}{100}\times x\right)=6$
⇒ x = $\left(6\times \frac{100}{12.5}\right)=\left(6\times 8\right)=48$
Hence, the value of x is 48.

Question 15:

What per cent of 84 is 14?

Answer 15:

Let x% of 84 be 14.
Then, $\left(\frac{x}{100}\times 84\right)=14$
⇒ $\frac{21x}{25}=14$
⇒ x = $\left(14\times \frac{25}{21}\right)=\left(\frac{2\times 25}{3}\right)=\frac{50}{3}=16\frac{2}{3}\%$
Hence, $16\frac{2}{3}\%$ of 84 is 14.

Question 16:

What percentage is

(i) Rs 15 of Rs 120?
(ii) 36 minutes of 2 hours?
(iii) 8 hours of 2 days
(iv) 160 metres of 4 km?
(v) 175 mL of 1 litre?
(vi) 25 paise of Rs 4?

Answer 16:

(i) Let x% of Rs 120 be Rs 15.
Then, Rs $\left(\frac{x}{100}\times 120\right)$ = Rs 15  
    ⇒ $\left(\frac{6x}{5}\right)$ = 15
    ∴ x = $\left(\frac{15\times 5}{6}\right)\%$ = $\left(\frac{25}{2}\right)\%$ = 12.5%
Hence, 12.5% of Rs 120 is Rs 15.

(ii) Let x% of 2 h be 36 min.
Then, $\left(\frac{x}{100}\times 2\times 60\right)$ min = 36 min
      ⇒ $\left(\frac{120x}{100}\right)$ = 36
     ∴ x = $\left(\frac{36\times 100}{120}\right)\%$ = 30%
Hence, 30% of 2 h is 36 min.

(iii) Let x% of 2 days be 8 h.
Then, $\left(\frac{x}{100}\times 2\times 24\right)$ h = 8 h
     ⇒ $\left(\frac{48x}{100}\right)$ = 8
     ∴ x = $\left(\frac{8\times 100}{48}\right)\%$ = $16\frac{2}{3}\%$
     Hence, $16\frac{2}{3}\%$ of 2 days is 8 h.

(iv) Let x% of 4 km be 160 m.
Then, $\left(\frac{x}{100}\times 4\times 1000\right)$ m = 160 m
     ⇒ 40x = 160
     ∴ x = $\left(\frac{160}{40}\right)\%$ = 4%
Hence, 4% of 4 km is 160 m.

(v) Let x% of 1 L be 175 mL.
Then, $\left(\frac{x}{100}\times 1\times 1000\right)$ mL = 175 mL
     ⇒ 10x  = 175
     ∴ x = $\left(\frac{175}{10}\right)\%$ = 17.5%
Hence, 17.5% of 1 L is 175 mL.

(vi) Let x% of Rs 4 be 25 paise.
Then, $\left(\frac{x}{100}\times 4\times 100\right)$ paise = 25 paise
     ⇒ 4x  = 25
     ∴ x = $\left(\frac{25}{4}\right)\%$ = $6\frac{1}{4}\%$
     Hence, $6\frac{1}{4}\%$ of Rs 4 is 25 paise.