Percentage - Aptitude MCQ Questions and Solutions with Explanations

Let B's Salary is Rs. 100. Then,
A's Salary = (100 + 25% of 100) = Rs. 125
Difference between A's Salary and B's Salary = 125 - 100 = Rs. 25
% Difference (lower) = $$\frac{{25}}{{125}} \times 100 = 20\% $$

Mind Calculation Method:
100(B salary) === 25%↑ ===> 125(A salary) === 20%↓ ===> 100 (B salary)
B's salary is 20% lower than A's

Net percentage increase in Population = (2.5 - 0.5) = 2% each year.
Let the Original Population of the town be 100.
Population of Town after 1 year = (100 + 2% of 100) = 102.
Population of the town after 2nd year = (102 + 2% of 102 ) = 104.04
Now, % increase in population = $$\frac{{4.04}}{{100}} \times 100 = 4.04\% $$

Mind Calculation Method:
100 == 2% Up(1^st year) ==> 102 == 2%Up(2^nd year) ==> 104.04
% population increase in 2 years = 4.04%.

Winner gets 65% of valid votes and loser gets 35% of votes
Difference between this two = 2748
(65-35)% = 2748
30% = 2748
Total number of voters, 100%
= $$\frac{{2748 \times 100}}{{30}}$$
= 9160

$$\eqalign{ & {\text{Let the present population of the town be }}P \cr & {\text{Using compound interest formula}} \cr & {\text{Then}}, \cr & P = x\left[ {1 + \left( {\frac{R}{{100}}} \right)} \right] - - - \,\left( i \right) \cr & {\text{And}}\,y = P\left[ {1 + \left( {\frac{R}{{100}}} \right)} \right] \cr & = P \times \frac{P}{x} - - - - \,\left( {ii} \right) \cr & {P^2} = xy; \cr & {\text{Hence}},\,P = \sqrt {xy} \cr} $$

Narayan's saving and rent = 1000 + 1800 = Rs. 2800
Let his monthly income be Rs. 100
30% of his income he spent on education i.e. Rs. 30
Remaining = 100 - 30 = 70
50% of remaining on food = $$\frac{{70 \times 50}}{{100}} = {\text{Rs}}{\text{. 35}}$$
Now, that 35 must be equal to his saving and rent i.e.
35 = 2800 then,
1 = $$\frac{{2800}}{{35}}$$
100 = $$\frac{{2800 \times 100}}{{35}} = {\text{Rs}}{\text{. 8000}}$$
So, his income = Rs. 8000

Let Q = 10.
Then, P = 60.
Q is 50 less than P.
Q, % less than P = $$\frac{{50}}{{60}} \times 100 = 83.33\% $$

Alternative Method
10 (Q) == (6 times greater) ==> 60(P) == x%↓(Less than Q) ==> 10 (Q)
Now,
$${\text{x}} = \frac{{50 \times 100}}{{60}} = 83.33\% $$

Let the third number be 100. Then,
1^st number = 130
2^nd number = 140
% 1^st number to the 2^nd number
$$\eqalign{ & = \frac{{130 \times 100}}{{140}} \cr & = \frac{{650}}{7} \cr & = 92\frac{6}{7}\% \cr} $$

$$\eqalign{ & {\text{Let number of men in the population be }}x \cr & {\text{Number of women}} = \left( {35000 - x} \right) \cr & {\text{Increase in the number of men}} \cr & = 6\% \,of\,x = \frac{{6x}}{{100}} \cr & {\text{Increase in the number of women}} \cr & = \left( {3500 - x} \right) \times \frac{4}{{100}} \cr & {\text{Increase in whole population}} \cr & = 36760 - 35000 = 1760 \cr & {\text{Now}}, \cr & \frac{{6x}}{{100}} + \left[ {\left( {35000 - x} \right) \times \frac{4}{{100}}} \right] = 1760 \cr & \left[ {\left( {6x - 4x} \right) + 35000 \times \frac{4}{{100}}} \right] = 1760 \cr & 2x + 35000 \times 4 = 1760 \times 100 \cr & 2x = 176000 - 35000 \times 4 \cr & x = 18000 \cr & {\text{Number}}\,{\text{of}}\,{\text{men}} = 18000 \cr & {\text{Number}}\,{\text{of}}\,{\text{women}} \cr & = 35000 - 18000 \cr & = 17000 \cr} $$

Let each side of the cuboid be 10 unit initially.
Initial Volume of the cuboid,
= length * breadth * height = 10 × 10 × 10 = 1000 cubic unit.
After increment dimensions become,
Length = (10 + 10% of 10) = 11 unit.
Breadth = (10 + 20% of 10) = 12 unit.
Height = (10 + 50% of 10) = 15 unit.
Now, present volume = 11 × 12 × 15 = 1980 cubic unit.
Increase in volume = 1980 - 1000 = 980 cubic unit.
% increase in volume = $$\frac{{980}}{{1000}} \times 100 = 98\% $$

Mind Calculation Method:
100 == 50%↑(height effects) ==> 150 == 20%↑(breadth) ==> 180 == 10%↑(length effects) ==> 198
Change in volume = 98%
[We can take net percentage change in any order]

Let Rs. 100 be spend on rice initially for 20 kg.
As the price falls by 20%, new price for 20 kg rice,
= (100 - 20% of 100) = 80
New price of rice = $$\frac{{80}}{{20}}$$ = Rs. 4 per kg.
Rice can bought now at = $$\frac{{100}}{{4}}$$ = 25 kg.