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 

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