Q.1 Convert each of the following into the fraction:

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

Q.2 Convert each of the following with percentage:

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

Q.3 Explain each of the following ratios on the percentage:

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

Q.4 Express each of the following decimal on the percentage:

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

Q.5 Express each of the following percentage in decimal:

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

Q.6 Express each of the following as ratio:

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

Q.7 Find the value of:

i) $33\% \hspace{5pt} of \hspace{5pt} Rs.50$

$33\% \hspace{5pt} of \hspace{5pt} Rs.50 = (\frac{33}{100} \times 50) = 16.50 Rs$

ii) $6\frac{2}{3}\% \hspace{5pt} of \hspace{5pt} 3 m$

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

iii) $0.6\% \hspace{5pt} of \hspace{5pt} 35 Kg$

$0.6\% \hspace{5pt} of \hspace{5pt} 35 Kg = (\frac{6}{10} \times \frac{35}{100}) = 0.21 kg = 210 gm$

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

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

Q8. Explain the Following:

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

$Let \hspace{5pt} x\% \hspace{5pt} 0f \hspace{5pt} Rs.\hspace{2pt} 9 = Rs.\hspace{2pt} 5$

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

ii) What percentage of 32 m in 80m?

$Let \hspace{5pt} x\% \hspace{5pt} 0f \hspace{5pt} 32\hspace{2pt}m = 80\hspace{2pt} m$

$Then, \frac{x}{100} \times 32 = 80 \hspace{5pt} or \hspace{5pt} x = \frac{80 \times 100}{32} = 250\%$

iii) What percentage of 50kg in 65kg?

$Let \hspace{5pt} x\% \hspace{5pt} 0f \hspace{5pt} 50\hspace{2pt}kg = 65\hspace{2pt} kg$

$Then, \frac{x}{100} \times 50 = 65 \hspace{5pt} or \hspace{5pt} x = \frac{65 \times 100}{50} = 130\%$

iv) What percentage of 5 Liters in 400ml?

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

$Then, \frac{x}{100} \times 5000 = 400 \hspace{5pt} or \hspace{5pt} x = \frac{400 \times 100}{5000} = 8\%$

Q9. Explain the Following:

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

Let the number to be $x$

$Then \hspace{5pt} \frac{8}{100}\times x = 24 \hspace{5pt} or \hspace{5pt} x = 100 \times \frac{24}{8} = 300$

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

Let the number to be $x$

$Then \hspace{5pt} \frac{7.25}{100}\times x = 2.9 \hspace{5pt} or \hspace{5pt} x = 40$

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

Let the number to be $x$

$Then \hspace{5pt} \frac{20}{3 \times 100}\times x = 1 \hspace{5pt} or \hspace{5pt} x = 15$

Q.10 Explain the following:

i) Increase 75 by 24%

$Required \hspace{5pt} Number = 75 \times (1+\frac{24}{100}) = 93$

ii) Decrease 375 by 8%

$Required \hspace{5pt} Number = 375 \times (1-\frac{8}{100}) = 345$

Q.11 What Number Increase by 15% Becomes 276%

Let the number to be $x$

$Then \hspace{5pt} x(1+\frac{15}{100})= 276 \hspace{5pt} or \hspace{5pt} x = 240$

Q.12 What Number when Decrease by 8% Becomes 345%

Let the number to be $x$

$Then \hspace{5pt} x(1-\frac{8}{100})= 345 \hspace{5pt} or \hspace{5pt} x = 375$