Percentage - Aptitude MCQ Questions and Solutions with Explanations

60% of 264
$$\eqalign{ & = \left( {\frac{{60}}{{100}} \times 264} \right) \cr & = 158.40 \cr} $$
10% of 44
$$\eqalign{ & = \left( {\frac{{10}}{{100}} \times 44} \right) \cr & = 4.40 \cr} $$
15% of 1056
$$\eqalign{ & = \left( {\frac{{15}}{{100}} \times 1056} \right) \cr & = 158.40 \cr} $$
30% of 132
$$\eqalign{ & = \left( {\frac{{30}}{{100}} \times 132} \right) \cr & = 39.60 \cr} $$
∴ 60% of 264 = 15% of 1056

Let the number be $$x$$
Then,
$$\eqalign{ & x - 16\% \,\,{\text{of}}\,x = 42 \cr & \Leftrightarrow x - \frac{{16}}{{100}}x = 42 \cr & \Leftrightarrow x - \frac{4}{{25x}} = 42 \cr & \Leftrightarrow \frac{{21}}{{25}}x = 42 \cr & \Leftrightarrow x = \left( {\frac{{42 \times 25}}{{21}}} \right) \cr & \Leftrightarrow x = 50 \cr} $$

$$\left( {23.6\% {\text{ of 1254}}} \right) - \left( {16.6\% {\text{ of 834}}} \right)$$
$$ = \left( {\frac{{236}}{{10}} \times \frac{1}{{100}} \times 1254} \right) - $$     $$\left( {\frac{{166}}{{10}} \times \frac{1}{{100}} \times 834} \right)$$
$$\eqalign{ & = \frac{1}{{1000}}\left( {236 \times 1254 - 166 \times 834} \right) \cr & = \frac{{12}}{{1000}}\left( {24662 - 11537} \right) \cr & = \left( {\frac{{12 \times 13125}}{{1000}}} \right) \cr & = 157.5 \cr} $$

Let the first number be x and the second number be y
$$\frac{1}{4}{\text{ of 60% of }}x = \frac{2}{5}{\text{ of 20% of }}y$$
$$\eqalign{ & \Rightarrow \frac{1}{4} \times \frac{{60}}{{100}} \times x = \frac{2}{5} \times \frac{{20}}{{100}} \times y \cr & \Rightarrow \frac{{3x}}{{20}} = \frac{{2y}}{{25}} \cr & \Rightarrow \frac{x}{y} = \frac{2}{{25}} \times \frac{{20}}{3} \cr & \Rightarrow \frac{x}{y} = \frac{8}{{15}} \cr} $$

Let number of students who appeared at the examination be $$x$$
Passed percentage = 96%
Failed percentage = 4%
According to given information we get
Unsuccessful students = 4%
∴ 4% of $$x$$ = 500
⇒ $$\left( {\frac{{x \times 4}}{{100}}} \right)$$  = 500
⇒ $$x$$ = $$\left( {\frac{{500 \times 100}}{{4}}} \right)$$
⇒ $$x$$ = 12500

Reduction in consumption :
$$\eqalign{ & = \left[ {\frac{R}{{\left( {100 + R} \right)}} \times 100} \right]\% \cr & = \left( {\frac{{15}}{{115}} \times 100} \right)\% \cr & = \frac{{300}}{{23}}\% \cr & = 13\frac{1}{{23}}\% \cr} $$

Let the number be x
Then,
$$\eqalign{ & 38\% {\text{ of }}x - 24\% \,\,{\text{of }}x = 135.10 \cr & \Rightarrow \frac{{38}}{{100}}x - \frac{{24}}{{100}}x = 135.10 \cr & \Rightarrow \frac{{14}}{{100}}x = 135.10 \cr & \Rightarrow x = \left( {\frac{{135.10 \times 100}}{{14}}} \right) \cr & \Rightarrow x = 965 \cr & \therefore 40\% {\text{ of 965 :}} \cr & = \left( {\frac{{40}}{{100}} \times 965} \right) \cr & = 386 \cr} $$

Let Raman's expense be Rs. $$x$$
Then, Vimal's expenses :
= 90% of $$x$$
$$\eqalign{ & = {\text{ Rs}}{\text{. }}\left( {\frac{{90}}{{100}} \times x} \right) \cr & = {\text{Rs}}{\text{. }}\frac{9}{{10}}x{\text{ }} \cr} $$
Aman's expense :
$$\eqalign{ & = {\text{130% of Rs}}{\text{. }}\left( {\frac{{9x}}{{10}}} \right) \cr & = {\text{ Rs}}{\text{. }}\left( {\frac{{130}}{{100}} \times \frac{{9x}}{{10}}} \right) \cr & = {\text{ Rs}}{\text{. }}\frac{{117x}}{{100}} \cr & \therefore \frac{{117x}}{{100}} + \frac{{9x}}{{10}} + x = 6447 \cr & \Rightarrow \frac{{117x + 90x + 100x}}{{100}} = 6447 \cr & \Rightarrow 307x = 644700 \cr & \Rightarrow x = \frac{{644700}}{{307}} \cr & \Rightarrow x = 2100 \cr & {\text{Hence, Aman's expenses :}} \cr & = {\text{Rs}}{\text{. }}\left( {\frac{{117 \times 2100}}{{100}}} \right) \cr & = {\text{Rs}}{\text{. 2457}} \cr} $$

$$\eqalign{ & A = 150\% {\text{ of }}B \cr & \Rightarrow A = \frac{{150}}{{100}}B \cr & \Rightarrow \frac{A}{B} = \frac{3}{2} \cr & \Rightarrow \frac{A}{B} + 1 = \frac{3}{2} + 1 \cr & \Rightarrow \frac{{A + B}}{B} = \frac{5}{2} \cr & \Rightarrow \frac{B}{{A + B}} = \frac{2}{5} \cr} $$
∴ Required percentage :
$$\eqalign{ & = \left( {\frac{B}{{A + B}} \times 100} \right)\% \cr & = \left( {\frac{2}{5} \times 100} \right)\% \cr & = 40\% \cr} $$

Let the total salary be Rs. $$x$$
Then,
(100 -10)% of (100 - 20)% of (100 - 20)% of (100 - 10)% of $$x$$ = 15552
$$ \Leftrightarrow \left( {\frac{{90}}{{100}} \times \frac{{80}}{{100}} \times \frac{{80}}{{100}} \times \frac{{90}}{{100}} \times x} \right)$$       $$ = 15552$$
$$\eqalign{ & \Leftrightarrow x = \left( {\frac{{15552 \times 10000}}{{64 \times 81}}} \right) \cr & \Leftrightarrow x = 30000 \cr} $$