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\%  

Answer:

\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}   

Answer:

\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}   

Answer:

\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} \%

\displaystyle  \\

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  

Answer:

\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\%

\displaystyle  \\

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\%  

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 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\%  

Answer:

\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

Answer:

\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?

Answer:

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.

Answer:

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\%

Answer:

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

\displaystyle  \\

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

Answer:

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\%

Answer:

Let the number to be \displaystyle  x

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