\displaystyle \textbf{Question 1: }\text{Convert each of the following into a fraction:}
\displaystyle \text{(i) }68\%\qquad \text{(ii) }3\frac{1}{3}\%\qquad \text{(iii) }224\%\qquad \text{(iv) }0.05\%
\displaystyle \text{Answer:}

\displaystyle \text{(i) }68\%=\frac{68}{100}=\frac{17}{25}.

\displaystyle \text{(ii) }3\frac{1}{3}\% =\frac{10}{3}\%=\frac{10}{3\times100}=\frac{1}{30}.

\displaystyle \text{(iii) }224\%=\frac{224}{100}=\frac{56}{25}.

\displaystyle \text{(iv) }0.05\%=\frac{0.05}{100} =\frac{5}{10000}=\frac{1}{2000}.
\displaystyle \\

\displaystyle \textbf{Question 2: }\text{Convert each of the following into a percentage:}
\displaystyle \text{(i) }\frac{2}{15}\qquad \text{(ii) }\frac{9}{40}\qquad \text{(iii) }1\frac{2}{3}\qquad \text{(iv) }2\frac{2}{5}
\displaystyle \text{Answer:}

\displaystyle \text{(i) }\frac{2}{15} =\left(\frac{2}{15}\times100\right)\%=\frac{40}{3}\%=13\frac{1}{3}\%.

\displaystyle \text{(ii) }\frac{9}{40} =\left(\frac{9}{40}\times100\right)\%=22.5\%.

\displaystyle \text{(iii) }1\frac{2}{3} =\left(\frac{5}{3}\times100\right)\%=166\frac{2}{3}\%.

\displaystyle \text{(iv) }2\frac{2}{5} =\left(\frac{12}{5}\times100\right)\%=240\%.
\displaystyle \\

\displaystyle \textbf{Question 3: }\text{Express each of the following ratios as a percentage:}
\displaystyle \text{(i) }13:20\qquad \text{(ii) }11:18\qquad \text{(iii) }87:25\qquad \text{(iv) }6\frac{1}{4}:4\frac{3}{8}
\displaystyle \text{Answer:}

\displaystyle \text{(i) }13:20 =\left(\frac{13}{20}\times100\right)\%=65\%.

\displaystyle \text{(ii) }11:18 =\left(\frac{11}{18}\times100\right)\%=61\frac{1}{9}\%.

\displaystyle \text{(iii) }87:25 =\left(\frac{87}{25}\times100\right)\%=348\%.

\displaystyle \text{(iv) }6\frac{1}{4}:4\frac{3}{8} =\frac{25}{4}:\frac{35}{8}.
\displaystyle =\left(\frac{25}{4}\times\frac{8}{35}\times100\right)\% =\frac{1000}{7}\%=142\frac{6}{7}\%.
\displaystyle \\

\displaystyle \textbf{Question 4: }\text{Express each of the following decimals as a percentage:}
\displaystyle \text{(i) }0.2\qquad \text{(ii) }0.06\qquad \text{(iii) }0.8\qquad \text{(iv) }2.4
\displaystyle \text{Answer:}

\displaystyle \text{(i) }0.2=0.2\times100\%=20\%.

\displaystyle \text{(ii) }0.06=0.06\times100\%=6\%.

\displaystyle \text{(iii) }0.8=0.8\times100\%=80\%.

\displaystyle \text{(iv) }2.4=2.4\times100\%=240\%.
\displaystyle \\

\displaystyle \textbf{Question 5: }\text{Express each of the following percentages as a decimal:}
\displaystyle \text{(i) }25\%\qquad \text{(ii) }4\%\qquad \text{(iii) }3\frac{1}{5}\%\qquad \text{(iv) }0.3\%
\displaystyle \text{Answer:}

\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\frac{1}{100}=\frac{16}{500}=0.032.

\displaystyle \text{(iv) }0.3\%=\frac{0.3}{100}=0.003.
\displaystyle \\

\displaystyle \textbf{Question 6: }\text{Express each of the following percentages as a ratio:}
\displaystyle \text{(i) }48\%\qquad \text{(ii) }26\frac{2}{3}\%\qquad \text{(iii) }0.06\%\qquad \text{(iv) }120\%
\displaystyle \text{Answer:}

\displaystyle \text{(i) }48\%=48:100=12:25.

\displaystyle \text{(ii) }26\frac{2}{3}\% =\frac{80}{3}:100=80:300=4:15.

\displaystyle \text{(iii) }0.06\%=0.06:100=6:10000=3:5000.

\displaystyle \text{(iv) }120\%=120:100=6:5.
\displaystyle \\

\displaystyle \textbf{Question 7: }\text{Find the value of each of the following:}
\displaystyle \text{(i) }33\%\text{ of Rs. }50\qquad \text{(ii) }6\frac{2}{3}\%\text{ of }3\text{ m}
\displaystyle \text{(iii) }0.6\%\text{ of }35\text{ kg}\qquad \text{(iv) }3\frac{1}{4}\%\text{ of }5\text{ litres}
\displaystyle \text{Answer:}

\displaystyle \text{(i) }33\%\text{ of Rs. }50 =\frac{33}{100}\times50=\text{Rs. }16.50.

\displaystyle \text{(ii) }6\frac{2}{3}\%\text{ of }3\text{ m} =\frac{20}{3}\%\text{ of }3\text{ m}.
\displaystyle =\frac{20}{3}\times\frac{3}{100}\text{ m} =\frac{1}{5}\text{ m}=20\text{ cm}.

\displaystyle \text{(iii) }0.6\%\text{ of }35\text{ kg} =\frac{0.6}{100}\times35\text{ kg}.
\displaystyle =0.21\text{ kg}=210\text{ g}.

\displaystyle \text{(iv) }3\frac{1}{4}\%\text{ of }5\text{ litres} =\frac{13}{4}\%\text{ of }5\text{ litres}.
\displaystyle =\frac{13}{4}\times\frac{5}{100}\text{ litres} =0.1625\text{ litres}=162.5\text{ ml}.
\displaystyle \\

\displaystyle \textbf{Question 8: }\text{Find the following percentages:}
\displaystyle \text{(i) What percentage of Rs. }9\text{ is Rs. }5\text{?}
\displaystyle \text{(ii) What percentage of }32\text{ m is }80\text{ m?}
\displaystyle \text{(iii) What percentage of }50\text{ kg is }65\text{ kg?}
\displaystyle \text{(iv) What percentage of }5\text{ litres is }400\text{ ml?}
\displaystyle \text{Answer:}

\displaystyle \text{(i) Let }x\%\text{ of Rs. }9=\text{Rs. }5.
\displaystyle \frac{x}{100}\times9=5.
\displaystyle x=\frac{5\times100}{9} =\frac{500}{9}=55\frac{5}{9}.
\displaystyle \therefore \text{Rs. }5\text{ is }55\frac{5}{9}\%\text{ of Rs. }9.

\displaystyle \text{(ii) Let }x\%\text{ of }32\text{ m}=80\text{ m}.
\displaystyle \frac{x}{100}\times32=80.
\displaystyle x=\frac{80\times100}{32}=250.
\displaystyle \therefore 80\text{ m is }250\%\text{ of }32\text{ m}.

\displaystyle \text{(iii) Let }x\%\text{ of }50\text{ kg}=65\text{ kg}.
\displaystyle \frac{x}{100}\times50=65.
\displaystyle x=\frac{65\times100}{50}=130.
\displaystyle \therefore 65\text{ kg is }130\%\text{ of }50\text{ kg}.

\displaystyle \text{(iv) }5\text{ litres}=5000\text{ ml}.
\displaystyle \text{Let }x\%\text{ of }5000\text{ ml}=400\text{ ml}.
\displaystyle \frac{x}{100}\times5000=400.
\displaystyle x=\frac{400\times100}{5000}=8.
\displaystyle \therefore 400\text{ ml is }8\%\text{ of }5\text{ litres}.
\displaystyle \\

\displaystyle \textbf{Question 9: }\text{Find the number in each of the following:}
\displaystyle \text{(i) If }8\%\text{ of a number is }24,\text{ find the number.}
\displaystyle \text{(ii) If }7.25\%\text{ of a number is }2.9,\text{ find the number.}
\displaystyle \text{(iii) If }6\frac{2}{3}\%\text{ of a number is }1,\text{ find the number.}
\displaystyle \text{Answer:}

\displaystyle \text{(i) Let the number be }x.
\displaystyle \frac{8}{100}\times x=24.
\displaystyle x=\frac{24\times100}{8}=300.
\displaystyle \therefore \text{the required number is }300.

\displaystyle \text{(ii) Let the number be }x.
\displaystyle \frac{7.25}{100}\times x=2.9.
\displaystyle x=\frac{2.9\times100}{7.25}=40.
\displaystyle \therefore \text{the required number is }40.

\displaystyle \text{(iii) Let the number be }x.
\displaystyle 6\frac{2}{3}\%=\frac{20}{3}\%=\frac{20}{300}=\frac{1}{15}.
\displaystyle \frac{1}{15}\times x=1.
\displaystyle x=15.
\displaystyle \therefore \text{the required number is }15.
\displaystyle \\

\displaystyle \textbf{Question 10: }\text{Find the following:}
\displaystyle \text{(i) Increase }75\text{ by }24\%.
\displaystyle \text{(ii) Decrease }375\text{ by }8\%.
\displaystyle \text{Answer:}

\displaystyle \text{(i) Increase}=24\%\text{ of }75 =\frac{24}{100}\times75=18.
\displaystyle \text{Required number}=75+18=93.
\displaystyle \text{Alternatively, required number} =75\left(1+\frac{24}{100}\right)=93.

\displaystyle \text{(ii) Decrease}=8\%\text{ of }375 =\frac{8}{100}\times375=30.
\displaystyle \text{Required number}=375-30=345.
\displaystyle \text{Alternatively, required number} =375\left(1-\frac{8}{100}\right)=345.
\displaystyle \\

\displaystyle \textbf{Question 11: }\text{What number when increased by }15\%\text{ becomes }276\text{?}
\displaystyle \text{Answer:}
\displaystyle \text{Let the required number be }x.
\displaystyle x+\frac{15}{100}x=276.
\displaystyle x\left(1+\frac{15}{100}\right)=276.
\displaystyle \frac{115}{100}x=276.
\displaystyle x=276\times\frac{100}{115}=240.
\displaystyle \therefore \text{the required number is }240.
\displaystyle \\

\displaystyle \textbf{Question 12: }\text{What number when decreased by }8\%\text{ becomes }345\text{?}
\displaystyle \text{Answer:}
\displaystyle \text{Let the required number be }x.
\displaystyle x-\frac{8}{100}x=345.
\displaystyle x\left(1-\frac{8}{100}\right)=345.
\displaystyle \frac{92}{100}x=345.
\displaystyle x=345\times\frac{100}{92}=375.
\displaystyle \therefore \text{the required number is }375.
\displaystyle \\

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