Percentage - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & 20\% \,{\text{of}}\,a = b \Rightarrow \frac{{20}}{{100}}a = b \cr & \therefore b\% \,{\text{of}}\,20 = {\frac{b}{{100}} \times 20} \cr & = {\frac{{20}}{{100}}a \times \frac{1}{{100}} \times 20} \cr & = \frac{4}{{100}}a = 4\% \,\,{\text{of }}\,a \cr} $$

Let the number of students be x. Then,
Number of students above 8 years of age
$$\eqalign{ & = \left( {100 - 20} \right)\% \,{\text{of}}\,\,x = 80\% \,\,{\text{of}}\,\,x \cr & \therefore 80\% \,{\text{of}}\,\,x = 48 + \frac{2}{3}\,{\text{of}}\,\,48 \cr & \Rightarrow \frac{{80}}{{100}}x = 80 \cr & \Rightarrow x = 100 \cr} $$

$$\eqalign{ & 5\% \,{\text{of}}\,A + 4\% \,{\text{of}}\,B = \frac{2}{3}\left( {6\% \,{\text{of}}\,A + \,8\,{\text{of}}\,B} \right) \cr & \Rightarrow \frac{5}{{100}}A + \frac{4}{{100}}B = \frac{2}{3}\left( {\frac{6}{{100}}A + \frac{8}{{100}}B} \right) \cr & \Rightarrow \frac{1}{{20}}A + \frac{1}{{25}}B = \frac{1}{{25}}A + \frac{4}{{75}}B \cr & \Rightarrow \left( {\frac{1}{{20}} - \frac{1}{{25}}} \right)A = \left( {\frac{4}{{75}} - \frac{1}{{25}}} \right)B \cr & \Rightarrow \frac{1}{{100}}A = \frac{1}{{75}}B \cr & \frac{A}{B} = \frac{{100}}{{75}} = \frac{4}{3} \cr & \therefore {\text{Required}}\,{\text{ratio}} = 4:3 \cr} $$

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{number}}\,{\text{be}}\,x \cr & {\text{Then,}}\,{\text{error}} = \frac{5}{3}x - \frac{3}{5}x = \frac{{16}}{{15}}x. \cr & {\text{Error}}\% = \left( {\frac{{16x}}{{15}} \times \frac{3}{{5x}} \times 100} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 64\% \cr} $$

Number of valid votes
= 80% of 7500
= 6000
∴ Valid votes polled by other candidate
= 45% of 6000
= $$ {\frac{{45}}{{100}} \times 6000} $$
= 2700

Total number of votes polled
= (1136 + 7636 + 11628)
= 20400
∴ Required percentage
= $$\left( {\frac{{11628}}{{20400}} \times 100} \right)\% $$
= $$57\% $$

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{sum}}\,{\text{paid}}\,{\text{to}}\,{\text{y}}\,{\text{per}}\,{\text{week}}\,{\text{be}}\,Rs.\,z \cr & {\text{Then}},\,z + 120\% \,of\,z = 550 \cr & \Rightarrow z + \frac{{120}}{{100}}z = 550 \cr & \Rightarrow \frac{{11}}{5}z = 550 \cr & \Rightarrow z = {\frac{{550 \times 5}}{{11}}} = 250 \cr} $$

Let the amount taxable purchases be Rs. x
$$\eqalign{ & {\text{Then}},6\% \,\,{\text{of}}\,x = \frac{{30}}{{100}} \cr & \Rightarrow x = {\frac{{30}}{{100}} \times \frac{{100}}{6}} = 5 \cr & \therefore {\text{Cost of tax free items}} \cr & = {\text{Rs}}{\text{.}}\left[ {25 - \left( {5 + 0.30} \right)} \right] \cr & = {\text{Rs}}{\text{.}}\,19.70 \cr} $$

$$\eqalign{ & {\text{Rebate}} = 6\% \,{\text{of Rs}}.6650 \cr & = {\text{Rs}}{\text{.}}\left( {\frac{6}{{100}} \times 6650} \right) \cr & = {\text{Rs}}{\text{.}}\,399 \cr & {\text{Sales tax}} = {\kern 1pt} 10\% \,{\text{of Rs}}{\text{.}}\left( {6650 - 399} \right) \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{10}}{{100}} \times 6251} \right) \cr & = {\text{Rs}}.625.10 \cr & \therefore {\text{Final}}{\kern 1pt} {\text{amount}} \cr & = {\text{Rs}}{\text{.}}\left( {6251 + 625.10} \right) \cr & = {\text{Rs}}{\text{.}}\,6876.10 \cr} $$

$$\eqalign{ & {\text{Increase}}\,{\text{in}}\,{\text{10}}\,{\text{years}} \cr & = {262500 - 175000} \cr & = 87500 \cr & {\text{Increase}}\% \cr & = \left( {\frac{{87500}}{{175000}} \times 100} \right)\% = 50\% \cr & \therefore {\text{Required}}\,{\text{average}} \cr & = {\frac{{50}}{{10}}} \% = 5\% \cr} $$