Percentage - Aptitude MCQ Questions and Solutions with Explanations

Answer: Option D

$$\eqalign{ & x\% {\text{ of 500 }} = y\% {\text{ of 300}} \cr & \Rightarrow \frac{x}{{100}} \times 500 = \frac{y}{{100}} \times 300 \cr & \Rightarrow 5x = 3y \cr & \Rightarrow y = \frac{5}{3}x \cr & x\% {\text{ of }}y\% {\text{ of 200}} = 60 \cr & \Rightarrow \frac{x}{{100}} \times \frac{y}{{100}} \times 200 = 60 \cr & \Rightarrow xy = 3000 \cr & \Rightarrow x \times \frac{5}{3}x = 3000 \cr & \Rightarrow {x^2} = 3000 \times \frac{3}{5} \cr & \Rightarrow {x^2} = 1800 \cr & \Rightarrow x = 30\sqrt 2 \cr} $$

Answer: Option B

Let the total population be x
Then, migrant population :
$$\eqalign{ & = 35\% {\text{ of }}x \cr & = \left( {\frac{{35}}{{100}} \times x} \right) \cr & = \frac{{7x}}{{20}} \cr} $$
Local population :
$$\eqalign{ & = \left( {x - \frac{{7x}}{{20}}} \right) \cr & = \frac{{13x}}{{20}} \cr} $$
Number of rural migrants :
$$\eqalign{ & = 20\% {\text{ of }}\frac{{7x}}{{20}} \cr & = \left( {\frac{{20}}{{100}} \times \frac{{7x}}{{20}}} \right) \cr & = \frac{{7x}}{{100}} \cr} $$
Number of urban migrants :
$$\eqalign{ & = \left( {\frac{{7x}}{{20}} - \frac{{7x}}{{100}}} \right) \cr & = \frac{{28x}}{{100}} \cr & = \frac{{7x}}{{25}} \cr} $$
Female population :
$$48\% {\text{ of }}\frac{{13x}}{{20}} + 30\% {\text{ of }}\frac{{7x}}{{100}}$$     $$ +\, 40\% {\text{ of }}\frac{{7x}}{{25}}$$
$$ = \left( {\frac{{48}}{{100}} \times \frac{{13x}}{{20}}} \right) + \left( {\frac{{30}}{{100}} \times \frac{{7x}}{{100}}} \right)$$      $$ + \left( {\frac{{40}}{{100}} \times \frac{{7x}}{{25}}} \right)$$
$$\eqalign{ & = \frac{{39x}}{{125}} + \frac{{21x}}{{1000}} + \frac{{14x}}{{125}} \cr & = \frac{{445x}}{{1000}} \cr} $$
∴ Required percentage :
$$\eqalign{ & = \left( {\frac{{445x}}{{1000}} \times \frac{1}{x} \times 100} \right)\% \cr & = 44.50\% \cr} $$

Answer: Option D

Let original income = Rs. 100
Then savings = Rs. 25 and expenditure = Rs. 75
New income = Rs. 120
New expenditure :
$$=$$ 115% of Rs. 75
$$\eqalign{ & = {\text{Rs}}{\text{. }}\left( {\frac{{115}}{{100}} \times 75} \right) \cr & = {\text{Rs}}{\text{. }}\frac{{345}}{4} \cr} $$
New saving :
. $$\eqalign{ & = {\text{Rs}}{\text{. }}\left( {120 - \frac{{345}}{4}} \right) \cr & = {\text{Rs}}{\text{. }}\frac{{135}}{4} \cr} $$
Increase in saving :
$$\eqalign{ & = {\text{Rs}}{\text{. }}\left( {\frac{{135}}{4} - 25} \right) \cr & = {\text{Rs}}{\text{. }}\frac{{35}}{4} \cr} $$
∴ Percentage increase :
$$\eqalign{ & = \left( {\frac{{35}}{4} \times \frac{1}{{25}} \times 100} \right)\% \cr & = 35\% \cr} $$

Answer: Option A

Population of 6 years ago :
$$\eqalign{ & = \left[ {\frac{{1771561}}{{{{\left( {1 + \frac{{10}}{{100}}} \right)}^6}}}} \right] \cr & = 1771561 \times {\left( {\frac{{10}}{{11}}} \right)^6} \cr & = \frac{{1771561 \times 1000000}}{{1771561}} \cr & = 1000000 \cr} $$

Answer: Option A

Let the original quantity be x kg.
Vanaspati ghee in x kg
$$\eqalign{ & = \left( {\frac{{40}}{{100}}x} \right){\text{kg}} \cr & = \left( {\frac{{2x}}{5}} \right){\text{kg}} \cr} $$
Now,
$$\eqalign{ & \Rightarrow \frac{{\frac{{2x}}{5}}}{{x + 10}} = \frac{{20}}{{100}} \cr & \Rightarrow \frac{{2x}}{{5x + 50}} = \frac{1}{5} \cr & \Rightarrow 5x = 50 \cr & \Rightarrow x = 10 \cr} $$