Question 1: Convert each of the following into the fraction:

i) 68\%          ii) 3 \frac{1}{3}          iii) 224\%           iv) 0.05\%  

Answer:

i) 68\% = \frac{68}{100} = 0.68

ii) 3 \frac{1}{3} = \frac{10}{3} \% = \frac{10}{3\times 100} = 0.033

iii) 224\% = \frac{224}{100} = 2.24

iv) 0.05\% = \frac{0.05}{100} = 0.0005

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Question 2: Convert each of the following with percentage:

i) \frac{2}{15}          ii) \frac{9}{40}          iii) 1 \frac{2}{3}          iv) 2 \frac{2}{5}  

Answer:

i) \frac{2}{15} = ( \frac{2}{15} \times 100 )\% = \frac{40}{3} \%

ii) \frac{9}{40} = ( \frac{9}{40} \times 100 )\% = 22.5 \%

iii) 1 \frac{2}{3} = ( \frac{5}{3} \times 100) \% = 166 \frac{2}{3} \%

iv) 2 \frac{2}{5} = ( \frac{12}{5} \times 100) \% = 240 \%

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Question 3: Explain each of the following ratios on the percentage:

i) 13 \colon 20          ii) 11 \colon 18           iii) 87 \colon 25           iv) 6 \frac{1}{4} \colon 4 \frac{3}{8}  

Answer:

i) 13 \colon 20 = ( \frac{13}{20} \times 100) \% = 65\%

ii) 11 \colon 18 = ( \frac{11}{18} \times 100) \% = 61 \frac{1}{9} \%

iii) 87 \colon 25 = ( \frac{87}{25} \times 100) \% = 348\%

iv) 6 \frac{1}{4} \colon 4 \frac{3}{8} = ( \frac{25}{4} \times \frac{8}{35} \times 100) \% = 142 \frac{6}{7} \%

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Question 4: Express each of the following decimal on the percentage:

i) 0.2           ii) 0.06           iii) 0.8           iv) 2.4  

Answer:

i) 0.2 = \frac{2}{10} = ( \frac{2}{10} \times 100) \% = 20\%

ii) 0.06 = \frac{6}{100} = ( \frac{6}{100} \times 100) \% = 6\%

iii) 0.8 = \frac{8}{1000} = ( \frac{8}{1000} \times 100) \% = 0.8\%

iv) 2.4 = \frac{24}{10} = ( \frac{24}{10} \times 100) \% = 240\%

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Question 5: Express each of the following percentage in decimal:

i) 25\%           ii) 4\%           iii) 3 \frac{1}{5} \%          iv) 0.3\%  

Answer:

i) 25\% = \frac{25}{100} = 0.25

ii) 4\% = \frac{4}{100} = 0.04

iii) 3 \frac{1}{5} \% = \frac{16}{5 \times 100} = 0.032

iv) 0.3\% = \frac{3}{10 \times 100} = 0.25

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Question 6: Express each of the following as ratio:

i) 48\%          ii) 26 \frac{2}{3} \%          iii) 0.06\%          iv) 120\%  

Answer:

i) 48\%= \frac{48}{100} = \frac{12}{25} = 12 \colon 25

ii) 26 \frac{2}{3} \%= \frac{80}{3} \% = \frac{80}{300} = 4 \colon 15

iii) 0.06\% = \frac{6}{100} \% = \frac{6}{100 \times 100} = 3 \colon 5000

iv) 120\%= \frac{120}{100} = 6 \colon 5

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Question 7: Find the value of:

i) 33\% \ of \ Rs. 50          ii) 6\frac{2}{3}\% \ of \ 3 \ m

iii) 0.6\% \ of \ 35 \ Kg          iv) 3 \frac{1}{4} \% \ of \ 5 \ Liters

Answer:

i) 33\% \ of \ Rs.\ 50

33\% \ of \ Rs.\ 50 = ( \frac{33}{100} \times 50) = 16.50 Rs

ii)6\frac{2}{3}\% \ of \ 3 \ m

6 \frac{2}{3} \% \ of \ 3 m = \frac{22}{3} \% \ of \ 3 m = ( \frac{22}{3} \times \frac{3}{100} ) = \frac{1}{5} m

iii) 0.6\% \ of \ 35 \ Kg

0.6\% \ of \ 35 Kg = ( \frac{6}{10} \times \frac{35}{100} ) = 0.21 kg = 210 \ gm

iv) 3 \frac{1}{4} \% \ of \ 5 \ Liters

3 \frac{1}{4} \% \ of \ 5 Liters = ( \frac{13}{14} \times \frac{5}{100} ) = 0.1625 Liters = 162.5 \ ml

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Question 8: Explain the Following:

i) What percentage of Rs. 9 in Rs. 5 ? ii) What percentage of 32 m in 80 m?

iii) What percentage of 50 kg in 65 kg? iv) What percentage of 5 Liters in 400 ml?

Answer:

i) What percentage of Rs. 9 in Rs. 5 ?

Let \ x\% \ 0f \ Rs.\ 9 = Rs.\ 5

Then, \frac{x}{100} \times 9 = 5 \ or \ x = \frac{5 \times 100}{9} = 55 \frac{5}{9}\%

ii) What percentage of 32 m in 80 m?

Let \ x\% \ 0f \ 32\hspace{2pt}m = 80\ m

Then, \frac{x}{100} \times 32 = 80 \ or \ x = \frac{80 \times 100}{32} = 250\%

iii) What percentage of 50 kg in 65 kg?

Let \ x\% \ 0f \ 50\hspace{2pt}kg = 65\ kg

Then, \frac{x}{100} \times 50 = 65 \ or \ x = \frac{65 \times 100}{50} = 130\%

iv) What percentage of 5 Liters in 400 ml?

Let \ x\% \ 0f \ 5\hspace{2pt}liters = 400\ ml

Then, \frac{x}{100} \times 5000 = 400 \ or \ x = \frac{400 \times 100}{5000} = 8\%

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Question 9: Explain the Following:

i) If 8 \% of a numbers in 24 , find the Number.

ii) If 7.25 \% of a numbers in 2.9 , find the Number.

iii) If 6 \frac{2}{3} \% of a number in 1, find the Number.

Answer:

i) If 8 \%  of a numbers in 24 , find the Number.

Let the number to be x

Then \frac{8}{100} \times x = 24 \ or \ x = 100 \times \frac{24}{8} = 300

ii) If 7.25% of a numbers in 2.9, find the Number.

Let the number to be x

Then \frac{7.25}{100} \times x = 2.9 \ or \ x = 40

iii) If 6 \frac{2}{3} \% of a number in 1, find the Number.

Let the number to be x

Then \frac{20}{3 \times 100} \times x = 1 \ or \ x = 15

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Question 10: Explain the following:

i) Increase 75 by 24\%            ii) Decrease 375 by 8\%

Answer:

i) Increase 75 by 24\%

Required  Number = 75 \times (1+ \frac{24}{100} ) = 93

ii) Decrease 375 by 8\%

Required  Number = 375 \times (1- \frac{8}{100} ) = 345

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Question 11: What Number Increase by 15\% Becomes 276\% .

Answer:

Let the number to be x

Then x(1+ \frac{15}{100} )= 276 \ or \ x = 240

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Question 12: What Number when Decrease by 8\% Becomes 345\%

Answer:

Let the number to be x

Then x(1- \frac{8}{100} )= 345 \ or \ x = 375