Percentage - Aptitude MCQ Questions and Solutions with Explanations

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

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 :
$$\eqalign{ & = \left( {\frac{{445x}}{{1000}} \times \frac{1}{x} \times 100} \right)\% \cr & = 44.50\% \cr} $$

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 :
$$\eqalign{ & = \left( {\frac{{35}}{4} \times \frac{1}{{25}} \times 100} \right)\% \cr & = 35\% \cr} $$

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

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,
$$\eqalign{ & \Rightarrow \frac{{\frac{{2x}}{5}}}{{x + 10}} = \frac{{20}}{{100}} \cr & \Rightarrow \frac{{2x}}{{5x + 50}} = \frac{1}{5} \cr & \Rightarrow 5x = 50 \cr & \Rightarrow x = 10 \cr} $$

Number of women = 40% of 200 = 80
Number of men = 200 - 80 = 120
Number of women lectures = $$\frac{1}{5}$$ of 80 = 16
Number of men lectures = 16 × 2 = 32
∴ Required percentage :
$$\eqalign{ & = \left( {\frac{{32}}{{120}} \times 100} \right)\% \cr & = \frac{{80}}{3}\% \cr & = 26\frac{2}{3}\% \approx 27\% \cr} $$

Let, his income be = Rs. 100
Saving = Rs. 10
Expenditure = Rs. 90
Increased income = Rs. 120
Increased expenditure = Rs. 110
Increased in expenditure :
$$\eqalign{ & = \frac{{110 - 90}}{{90}} \times 100 \cr & = \frac{{200}}{9} \cr & = 22\frac{2}{9}\% \cr} $$

Quantity of alcohol in 10 c.c. solution
= (20% of 6 + 60% of 4) c.c.
= $$\left( {\frac{{20}}{{100}} \times 6 + \frac{{60}}{{100}} \times 4} \right)$$    c.c.
= (1.2 + 2.4) c.c.
= 3.6 c.c.
∴ Required strength :
$$\eqalign{ & = \left( {\frac{{3.6}}{{10}} \times 100} \right)\% \cr & = 36\% \cr} $$

Actual price :
$$= Rs. (25 + 2.5)$$
$$= Rs. 27.50$$
∴ Saving :
$$\eqalign{ & = \left( {\frac{{2.50}}{{27.50}} \times 100} \right)\% \cr & = \frac{{100}}{{11}}\% \cr & = 9\frac{1}{{11}}\% \approx 9\% \cr} $$

Let the worth of the house be Rs. x
Then,
$$\frac{2}{7}$$% of x = 28000
$$\eqalign{ & \Rightarrow \left( {\frac{2}{7} \times \frac{1}{{100}} \times x} \right) = 2800 \cr & \Rightarrow x = \left( {\frac{{2800 \times 100 \times 7}}{2}} \right) \cr & \Rightarrow x = 980000 \cr} $$