Percentage - Aptitude MCQ Questions and Solutions with Explanations

Let V denote the volume of 1 c.c. of water
Then, volume of ice formed from it :
= 109% of V = $$\frac{109}{100}$$V
When this ice change into water, decrease in volume :
= $$\frac{109}{100}$$V - V = $$\frac{9}{100}$$V
∴ Decrease % :
$$\eqalign{ & = \left( {\frac{{9V}}{{100}} \times \frac{{100}}{{109V}} \times 100} \right)\% \cr & = \frac{{900}}{{109}}\% \cr & = 8\frac{{28}}{{109}}\% \cr} $$

Percentage annual increase
$$\eqalign{ & = \left( {\frac{1}{8} \times 100} \right)\% \cr & = \frac{{25}}{2}\% \cr} $$
Height after $$2\frac{1}{2}$$ years
$$\eqalign{ & = \left[ {8{{\left( {1 + \frac{{25}}{{2 \times 100}}} \right)}^2}\left( {1 + \frac{{25}}{{4 \times 100}}} \right)} \right]m \cr & = \left( {8 \times \frac{9}{8} \times \frac{9}{8} \times \frac{{17}}{{16}}} \right)m \cr & = \left( {\frac{{1377}}{{128}}} \right)m \cr & = 10.75\,\,m \cr} $$

Let x litres of 30% alcohol solution be added.
Then, 30% of x + 60% of 40 = 50% of (x + 40)
⇒ 30x + 60 × 40 = 50 (x + 40)
⇒ 30x + 2400 = 50x + 2000
⇒ 20x = 400
⇒ x = 20

Give (180% of ?) ÷ 2 = 504
⇒ ? × $$\frac{180}{100}$$ × 2 = 504
⇒ ? × $$\frac{180}{100}$$ = 504 × 2
⇒ ? × $$\frac{180}{100}$$ = 1008
⇒ ? = $$\frac{1008 × 100}{180}$$   = 560

Marked price of an article = Rs. 2400
According to the question,
2400 × (100 - x)% of 85% = 1876.80
⇒ 2400 × $$\frac{100 - x}{100}$$ × $$\frac{85}{100}$$ = 1876.80
⇒ (100 - x) = $$\frac{1876.80 × 100 × 100}{2400 × 85}$$
⇒ (100 - x) = $$\frac{18768000}{204000}$$
⇒ (100 - x) = 92
⇒ x = 100 - 92
⇒ x = 8%

Required percentage :
$$\eqalign{ & = \left( {\frac{5}{{2250}} \times 100} \right)\% \cr & = \frac{2}{9}\% \cr} $$

Number of sweets obtained by each student :
= 20% of 65
= 13
Number of sweets obtained by each teacher :
= 40% of 65
= 26
∴ Total number of sweets
= 65 × 13 + 4 × 26
= 845 + 104
= 949

Let the number be x
Then, 35% of x = 175
⇔ $$\frac{35}{100}$$ × x = 175
⇔ $$\frac{175 × 100}{35}$$   = 500
Now, let y% of 175 = 500
Then, $$\frac{y}{100}$$ × 175 = 500
⇔ y = $$\frac{500 × 100}{175}$$
⇔ y = $$\frac{2000}{7}$$
⇔ y = $$285\frac{5}{7}$$

Let the number be x
Then, x - 25% of x = 225
⇒ x - $$\frac{25}{100}$$x = 225
⇒ $$\frac{75x}{100}$$ = 225
⇒ x = $$\frac{225 × 100}{75}$$
⇒ x = 300
Required increase :
= (390 - 300)
= 90
∴ Increase % :
$$\eqalign{ & = \left( {\frac{{90}}{{300}} \times 100} \right)\% \cr & = 30\% \cr} $$

Let the maximum marks be = x
Then, 5% of x = 296 - 259
⇒ $$\frac{5x}{100}$$ = 37
⇒ x = $$\frac{37 × 100}{5}$$
⇒ x = 740