Percentage - Aptitude MCQ Questions and Solutions with Explanations

1

In an examination, 35% candidates failed in one subject and 42% failed in another subject while 15% failed in both the subjects. If 2500 candidates appeared at the examination, how many passed in either subject but not in both ?

A) 325 B) 1175 C) 2125 D) None of these

Discuss

Answer & Solution

Answer: Option B

Solution:

Failed in 1^st subject = $$\frac{35}{100}$$ × 2500 = 875
Failed in 2^nd subject = $$\frac{42}{100}$$ × 2500 = 1050
Failed in both = $$\frac{15}{100}$$ × 2500 = 375
Failed in 1^st subject only = (875 - 375) = 500
Failed in 2^nd subject only = (1050 - 375) = 675
∴ Passed in 2^nd only + Passed in 1^st only
= (675 + 500)
= 1175

2

14% of 14 + 28% of 28 + 92% of 96 - 15% of 85 = ?

A) 8.37 B) 85.37 C) 89.37 D) None of these

Discuss

Answer & Solution

Answer: Option B

Solution:

It is given that,
(14% of 14) + (28% of 28) + (92% of 96) - (15% of 85) = ?
$$\left( ? \right) = \left( {\frac{{14 \times 14}}{{100}}} \right) + \left( {\frac{{28 \times 28}}{{100}}} \right) + $$ $$\left( {\frac{{92 \times 96}}{{100}}} \right) - \left( {\frac{{15 \times 85}}{{100}}} \right)$$
$$\eqalign{ & \left( ? \right) = \left( {1.96 + 7.84 + 88.32 - 12.75} \right) \cr & \left( ? \right) = \left( {98.12 - 12.75} \right) \cr & \left( ? \right) = 85.37 \cr} $$

3

What percent of 88 is 33 ?

A) 34.5% B) 35.5% C) 36.5% D) 37.5%

Discuss

Answer & Solution

Answer: Option D

Solution:

Required percentage :
$$\eqalign{ & = \left( {\frac{{33}}{{88}} \times 100} \right)\% \cr & = \frac{{75}}{2}\% \cr & = 37.5\% \cr} $$

4

40% of 60% of $$\frac{3}{5}$$th of a number is 504. What is 25% of $$\frac{2}{5}$$th of that number ?

A) 175 B) 180 C) 350 D) 360 E) None of these

Discuss

Answer & Solution

Answer: Option C

Solution:

Let the number be x
Then, 40% of 60% of $$\frac{3}{5}$$ of x = 504
⇒ $$\frac{40}{100}$$ × $$\frac{60}{100}$$ × $$\frac{3}{5}$$ × x = 504
⇒ $$\frac{18}{125}$$x = 504
⇒ x = $$\frac{504 × 125}{18}$$
⇒ x = 3500
∴ 25% of $$\frac{2}{5}$$ of 3500 :
= $$\frac{25}{100}$$ × $$\frac{2}{5}$$ × 3500
= 350

5

Nupur invests Rs. 89856, which is 26% of her annual income, in mutual funds. What is her monthly income ?

A) Rs. 2398.50 B) Rs. 28800 C) Rs. 28990 D) Rs. 33606.25 E) None of these

Discuss

Answer & Solution

Answer: Option B

Solution:

Let Nupur's annual salary be Rs. x
Then, 26% of x = 89856
⇒ $$\frac{26x}{100}$$ = 89856
⇒ x = $$\frac{89856 × 100}{26}$$
⇒ x = 345600
∴ Nupur's monthly income :
= Rs. $$\frac{345600}{12}$$
= Rs. 28800

6

Two numbers A and B are such that the sum of 5% of A and 4% of B is two-thirds of the sum of 6% of A and 8% of B. Find the ratio of A : B ?

A) 2 : 3 B) 1 : 1 C) 3 : 4 D) 4 : 3

Discuss

Answer & Solution

Answer: Option D

Solution:

5% of A + 4% of B = $$\frac{2}{3}$$ (6% of A + 8% of B)
$$ \Leftrightarrow \frac{5}{{100}}A + \frac{4}{{100}}B = $$ $$\frac{2}{3}\left( {\frac{6}{{100}}A + \frac{8}{{100}}B} \right)$$
$$\eqalign{ & \Leftrightarrow \frac{1}{{20}}A + \frac{1}{{25}}B = \frac{1}{{25}}A + \frac{4}{{75}}B \cr & \Leftrightarrow \left( {\frac{1}{{20}} - \frac{1}{{25}}} \right)A = \left( {\frac{4}{{75}} - \frac{1}{{25}}} \right)B \cr & \Leftrightarrow \frac{1}{{100}}A = \frac{1}{{75}}B \cr & \Leftrightarrow \frac{A}{B} = \frac{{100}}{{75}} \cr & \Leftrightarrow \frac{A}{B} = \frac{4}{3} \cr} $$
∴ A : B = 4 : 3

7

In a college election between two candidates, one candidate got 55% of the total valid votes. 15% of the votes were invalid. If the total votes were 15200, what is the number of valid votes the other candidate got ?

A) 5814 B) 6840 C) 7106 D) 8360 E) None of these

Discuss

Answer & Solution

Answer: Option A

Solution:

Number of valid votes
= (100 - 15)% of 15200
= 85% of 15200
= $$\frac{85}{100}$$ × 15200
= 12920
Valid votes polled by other candidate :
= (100 - 55)% of 12920
= $$\frac{45}{100}$$ × 12920
= 5814

8

If x% of y is equal to z, what percent of z is x ?

A) $$\frac{{{y^2}}}{{100}}$$ % B) $$\frac{y}{{{{100}^2}}}$$ % C) $$\frac{{100}}{y}$$ % D) $$\frac{{{{100}^2}}}{y}$$ %

Discuss

Answer & Solution

Answer: Option D

Solution:

x% of y = z
⇒ $$\frac{x}{100}$$y = z
⇒ $$\frac{x}{z}$$ = $$\frac{100}{y}$$
∴ Required percentage
$$\eqalign{ & = \left( {\frac{x}{z} \times 100} \right)\% \cr & = \left( {\frac{{100}}{y} \times 100} \right)\% \cr & = \left( {\frac{{{{100}^2}}}{y}} \right)\% \cr} $$

9

A part of Rs. 9600 is invested at a 5% annual return, while the remainder is invested at a 3% annual return. If the annual income from both portions is the same, what is the total income from the two investments ?

A) Rs. 320 B) Rs. 380 C) Rs. 410 D) Rs. 440 E) None of these

Discuss

Answer & Solution

Answer: Option E

Solution:

Let the sum invested at 5% be Rs. x and that invested at 3% be Rs. (9600 - x)
Then, 5% of x = 3% of (9600 - x)
⇒ 5x = 3 (9600 - x)
⇒ 8x = 28800
⇒ x = 3600
Hence, total income :
= 5% of x + 3% of (9600 - x)
= Rs. (5% of 3600 + 3% of 6000)
= Rs. (180 + 180)
= Rs. 360

10

Of the 50 researchers in a work group, 40% will be assigned to Team A and the remaining 60% to Team B. However, 70% of the researchers prefer team A and 30% prefer Team B. What is the least possible number of researchers who will not be assigned to the team they prefer ?

A) 15 B) 20 C) 30 D) 35

Discuss

Answer & Solution

Answer: Option A

Solution:

Number of researchers who prefer Team A = 70% of 50 = 35
Number of researchers who prefer Team B = (50 - 35) = 15
Number of researchers assigned to Team A = 40% of 50 = 20
Number of researchers assigned to Team B = (50 - 20) = 30
To find the least possible number of researchers who will not be assigned to the team they prefer, we assume that the maximum number of researchers get the team they prefer.
So,Number of researchers who are assigned to the team they prefer = 20 (Team A) + 15 (Team B) = 35
∴ Required number = (50 - 35) = 15