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

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

$\displaystyle \text{i) } 68\% = \frac{68}{100} = 0.68$

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

$\displaystyle \text{iii) } 224\% = \frac{224}{100} = 2.24$

$\displaystyle \text{iv) } 0.05\% = \frac{0.05}{100} = 0.0005$

$\displaystyle \\$

Question 2: Convert each of the following with percentage:

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

$\displaystyle \text{i) } \frac{2}{15} = \Big( \frac{2}{15} \times 100 \Big) \% = \frac{40}{3} \%$

$\displaystyle \text{ii) } \frac{9}{40} = \Big( \frac{9}{40} \times 100 \Big) \% = 22.5 \%$

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

$\displaystyle \text{iv) } 2 \frac{2}{5} = \Big( \frac{12}{5} \times 100 \Big) \% = 240 \%$

$\displaystyle \\$

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

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

$\displaystyle \text{i) } 13 \colon 20 = \Big( \frac{13}{20} \times 100 \Big) \% = 65\%$

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

$\displaystyle \text{iii) } 87 \colon 25 = \Big( \frac{87}{25} \times 100 \Big) \% = 348\%$

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

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

$\displaystyle \text{i) } 0.2$        $\displaystyle \text{ii) } 0.06$        $\displaystyle \text{iii) } 0.8$        $\displaystyle \text{iv) } 2.4$

$\displaystyle \text{i) } 0.2 = \frac{2}{10} = \Big( \frac{2}{10} \times 100 \Big) \% = 20\%$

$\displaystyle \text{ii) } 0.06 = \frac{6}{100} = \Big( \frac{6}{100} \times 100 \Big) \% = 6\%$

$\displaystyle \text{iii) } 0.8 = \frac{8}{1000} = \Big( \frac{8}{1000} \times 100 \Big) \% = 0.8\%$

$\displaystyle \text{iv) } 2.4 = \frac{24}{10} = \Big( \frac{24}{10} \times 100 \Big) \% = 240\%$

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

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

$\displaystyle \text{i) } 25\% = \frac{25}{100} = 0.25$

$\displaystyle \text{ii) } 4\% = \frac{4}{100} = 0.04$

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

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

$\displaystyle \\$

Question 6: Express each of the following as ratio:

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

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

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

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

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

$\displaystyle \\$

Question 7: Find the value of:

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

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

$\displaystyle \text{i) } 33\% \ of \ Rs.\ 50$

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

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

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

$\displaystyle \text{iii) } 0.6\% \ of \ 35 \ Kg$

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

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

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

$\displaystyle \\$

Question 8: Explain the Following:

i) What percentage of Rs. $\displaystyle 9$ in Rs. $\displaystyle 5$ ?

ii) What percentage of $\displaystyle 32$ m in $\displaystyle 80$ m?

iii) What percentage of $\displaystyle 50$ kg in $\displaystyle 65$ kg?

iv) What percentage of $\displaystyle 5$ Liters in $\displaystyle 400$ ml?

i) What percentage of Rs. $\displaystyle 9$ in Rs. $\displaystyle 5$?

$\displaystyle \text{Let } x \% \text{ of Rs. } 9 = \text{ Rs. } 5$

$\displaystyle \text{Then } \frac{x}{100} \times 9 = 5 \text{ or } x = \frac{5 \times 100}{9} = 55 \frac{5}{9}\%$

ii) What percentage of $\displaystyle 32 \text{ m }$   in $\displaystyle 80 \text{ m }$  ?

$\displaystyle \text{Let } x\% \text{ of 32 m } = 80 \text{ m }$

$\displaystyle \text{Then } \frac{x}{100} \times 32 = 80 \text{ or } x = \frac{80 \times 100}{32} = 250\%$

iii) What percentage of $\displaystyle 50$ kg in $\displaystyle 65$ kg?

$\displaystyle \text{Let } x\% \text{ of 50 kg} = 65\ kg$

$\displaystyle \text{Then } \frac{x}{100} \times 50 = 65 \text{ or } x = \frac{65 \times 100}{50} = 130\%$

iv) What percentage of $\displaystyle 5$ Liters in $\displaystyle 400 \text{ m }$  l?

Let $\displaystyle x\% \text{ of 5 liters} = 400 \text{ ml }$

$\displaystyle \text{Then } \frac{x}{100} \times 5000 = 400 \text{ or } x = \frac{400 \times 100}{5000} = 8\%$

$\displaystyle \\$

Question 9: Explain the Following:

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

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

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

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

Let the number to be $\displaystyle x$

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

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

Let the number to be $\displaystyle x$

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

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

Let the number to be $\displaystyle x$

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

$\displaystyle \\$

Question 10: Explain the following:

i) Increase $\displaystyle 75$ by $\displaystyle 24\%$

ii) Decrease $\displaystyle 375$ by $\displaystyle 8\%$

i) Increase $\displaystyle 75$ by $\displaystyle 24\%$

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

ii) Decrease $\displaystyle 375$ by $\displaystyle 8\%$

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

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

Let the number to be $\displaystyle x$

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

$\displaystyle \\$

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

Let the number to be $\displaystyle x$
$\displaystyle \text{Then } x(1- \frac{8}{100} )= 345 \ or \ x = 375$