Percentage - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & 12\% \to \frac{{ + 3}}{{25}} \cr & 8\% \to \frac{{ - 2}}{{25}} \cr & {\text{Length}} \to 25:28 \cr & \underline {{\text{Breadth}} \to 25:23} \cr} $$

$${\text{Increase }}\% = \frac{{19}}{{625}} \times 100 = 3.04\% $$

Let total vote = 100
Invalid vote = 5
Raju got = 30
Ravi got = 32
Ashok got = 95 - (30 + 32) = 33
33 - 30 = 3 unit → 5136
1 unit → $$\frac{{5136}}{3}$$
100 unit → 171200

Calculation:
30% of the students from school X failed
Let the number of students from school X be 100
⇒ Number of students who failed = 30
⇒ Number of students who passed = (100 - 30) = 70
According to the question,
150% more students than school X, appeared in the examination from school Y
Number of students from school Y = $$100 + \left( {100 \times \frac{{150}}{{100}}} \right)$$
⇒ Number of students from school Y = 250
Again, according to the question,
80% of the total number of students from X and Y passed
Total students from school X and Y = 100 + 250 = 350
⇒ Total number of students who passed = $$350 \times \frac{{80}}{{100}}$$
⇒ Total number of students who passed = 280
Now,
Number of students who passed from school Y = 280 - 70
⇒ Number of students who passed from school Y = 210
Number of students who failed from school Y = 250 - 210
⇒ Number of students who failed from school Y = 40
Percentage of students who failed from Y = $$\frac{{40}}{{250}} \times 100$$
⇒ Percentage of students who failed from Y = 16%
∴ 16% of students failed from school Y.

$$66\frac{2}{3}\% = \frac{2}{3}$$
Saving = 3; Expenditure = 3 + 2 = 5
Income = 5 + 3 = 8
\[\begin{array}{*{20}{c}} {{\text{Income}}}& = &{{\text{Expenditure}}}& + &{{\text{Saving}}} \\ 8& = &5& + &3 \\ {800}& = &{500}& + &{300} \\ {\,\,\,\,\,\,\,\,\,\,\,\,\, \downarrow + 44\% }&{}&{\,\,\,\,\,\,\,\,\,\,\,\,\, \downarrow + 60\% }&{}&{} \\ {352}& = &{300}& + &x \end{array}\]
x = 352 - 300 = 52
52 units → 1040
1 unit → 20
500 units → 500 × 20 = 10,000

Given:
For Discount = 5%, Profit = 14%
Formula used:
Selling price = Marked price - Discount
Cost price = $$\frac{{100}}{{100 + {\text{Profit}}}} \times {\text{Selling price}}$$
Profit % = $$\frac{{{\text{Selling price}} - {\text{Cost price}}}}{{{\text{Cost price}}}} \times 100$$
Calculation:
Let the Marked price of the article = Rs. 100
Discount = 5% ⇒ Selling price = Rs. 95
Profit = 14% ⇒ Cost price = $${\text{Rs}}{\text{. }}\left( {\frac{{100}}{{100 + 14}}} \right) \times 95$$
Cost price = $${\text{Rs}}{\text{. }}\frac{{250}}{3}$$  = Rs. 83.3
For the Discount of 11%, Selling price = Rs. 89
Then Profit % = $$\frac{{89 - 83.3}}{{83.3}} \times 100$$
Profit = 6.84 ≈ 6.8
Hence, the correct answer is option A.

$$35\% = \frac{7}{{20}},\,15\% = \frac{3}{{20}}$$

$$\eqalign{ & \Rightarrow 90\% = 42210 \cr & \Rightarrow 100\% = \frac{{42210}}{{90}} \times 100 = 46900 \cr} $$

Raw material → 25% increase

Let monthly salary = 100x
Total expenditure = (40 + 18 + 12 + 5)x = 75x
25x = 20,000 - 16,000
x $$ = \frac{{4000}}{{25}} = 160$$
Hence monthly salary = 100x = 100 × 160 = 16,000

$$4\% \to \frac{{ - 1}}{{25}}$$

Given:
Percentage increase in the price of diesel = 26%
Percentage increase in total expenditure = 15%
Concept used:
P × C = E
Where P is Price, C is Consumption and E is Expenditure
Calculation:
Let initial price be P₁, consumption be C₁, and expenditure be E₁
P₁ × C₁ = E₁
⇒ $${{\text{C}}_1} = \frac{{{{\text{E}}_1}}}{{{{\text{P}}_1}}}$$
Let new price be P₂, new quantity consumed be C₂, and new expenditure be E₂
P₂ = P₁ + 26% of P₁
⇒ P₂ = 1.26P₁
E₂ = E₁ + 15% of E₁
⇒ E₂= 1.15E₁
As, P₂ × C₂ = E₂
⇒ 1.26P₁ × C₂ = 1.15E₁
⇒ C₂ = $$\frac{{{\text{1}}{\text{.15}}{{\text{E}}_1}}}{{{\text{1}}{\text{.26}}{{\text{P}}_1}}}$$
⇒ C₂ = 0.9126 × $$\frac{{{{\text{E}}_1}}}{{{{\text{P}}_1}}}$$
⇒ C₂ = 0.9126C₁
Decrease in consumption = C₁ - C₂
⇒ Decrease in consumption = C₁ - 0.9126C₁ = 0.0874C₁
Percentage decrease in consumption = $$\frac{{{\text{Decrease in consumption}}}}{{{\text{Initial consumption}}}} \times 100$$
⇒ Percentage decrease in consumption = $$\frac{{0.0874{{\text{C}}_1}}}{{{{\text{C}}_1}}} \times 100$$
∴ The percentage decrease in consumption is 8.7% (correct to 1 decimal place)