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

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

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) $2$ $\frac{2}{5}$

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) $6$ $\frac{1}{4}$ $\colon 4$ $\frac{3}{8}$

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) $2.4$

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) $0.3\%$

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) $120\%$

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

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?

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.

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 $8\%$

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 $276\%$.

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 $345\%$

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