Percentage - Aptitude MCQ Questions and Solutions with Explanations

1

In an election, 30% of the voters voted for candidate A whereas 60% of the remaining voted for candidate B. The remaining voters did not vote. If the difference between those who voted for candidate A and those who did not vote was 1200, how many individuals were eligible for casting vote in that election ?

A) 10000 B) 45000 C) 60000 D) 72000

Discuss

Answer & Solution

Answer: Option C

Solution:

Let the number of persons eligible to vote be x
Then, votes who voted for A = 30% of x
Votes who voted for B = 60% of (70% of x)
= $$\left( {\frac{{60}}{{100}} \times \frac{{70}}{{100}} \times 100} \right)$$ % of x
= 42% of x
Voters who did not vote = [100 - (30 + 42)]% of x = 28% of x
∴ 30% of x - 28% of x = 1200
⇒ 2% of x = 1200
⇒ x = $$\left( {\frac{{1200 × 100}}{{2}}} \right)$$
⇒ x = 60000

2

x% of x is the same as 10% of

A) $$\frac{{x}}{{10}}$$ B) $$\frac{{{x^2}}}{{10}}$$ C) $$\frac{{{x^3}}}{{10}}$$ D) None of these

Discuss

Answer & Solution

Answer: Option B

Solution:

Let x% of x = 10% of y
Then,
$$\eqalign{ & \Rightarrow \frac{x}{{100}} \times x = \frac{{10}}{{100}} \times y \cr & \Rightarrow y = \frac{{{x^2}}}{{100}} \times 10 \cr & \Rightarrow y = \frac{{{x^2}}}{{10}} \cr} $$

3

In a certain organisation, 40% employees are matriculates, 50% of the remaining are graduates and the remaining 180 are post-graduates. What is the number of graduate employees ?

A) 180 B) 240 C) 300 D) 360

Discuss

Answer & Solution

Answer: Option A

Solution:

Let the total number of employees be x
Then,
(100 - 50)% of (100 - 40)% of x = 180
50% of 60% of x = 180
$$\eqalign{ & \Rightarrow \left( {\frac{{50}}{{100}} \times \frac{{60}}{{100}} \times x} \right) = 180 \cr & \Rightarrow x = \left( {\frac{{180 \times 10}}{3}} \right) \cr & \Rightarrow x = 600 \cr} $$
∴ Number of graduate employees :
$$=$$ 50% of 60% of x
$$\eqalign{ & = \left( {\frac{{50}}{{100}} \times \frac{{60}}{{100}} \times 600} \right) \cr & = 180 \cr} $$

4

In an examination in which full marks were 800, A gets 20% more than B, B gets 20% more than C, and C gets 15% less than D. If A got 576, what percentage of full marks did D get (approximately) ?

A) 45.73 B) 51.27 C) 58.82 D) 61.71

Discuss

Answer & Solution

Answer: Option C

Solution:

$$\eqalign{ & A = \frac{{120}}{{100}}B, \cr & B = \frac{{120}}{{100}}C\, \& \cr & C = \frac{{85}}{{100}}D \cr & \therefore B = \frac{5}{6}A \cr & C = \frac{5}{6}B\, \& \cr & D = \frac{{20}}{{17}}C \cr & B = \frac{5}{6} \times 576 = 480 \cr & C = \frac{5}{6} \times 480 = 400 \cr & D = \frac{{20}}{{17}} \times 400 = \frac{{8000}}{{17}} \cr} $$
So, required percentage :
$$\eqalign{ & = \left( {\frac{{8000}}{{17}} \times \frac{1}{{800}} \times 100} \right)\% \cr & = 58.82\% \cr} $$

5

The price of an article is reduced by 25%. In order to retain the original price, the present price has to be increased by :

A) 20% B) 25% C) 33$$\frac{1}{3}$$% D) 50%

Discuss

Answer & Solution

Answer: Option C

Solution:

Let the original price = Rs. 100
New price = Rs. 75
Increase on 75 = 25
Increase on 100 :
$$\eqalign{ & = \left( {\frac{{25}}{{75}} \times 100} \right)\% \cr & = \frac{{100}}{3}\% \cr & = 33\frac{1}{3}\% \cr} $$

6

A person's salary is decreased by steps of 20%, 15% and 10%. Approximately by what percent should the reduced salary be increases so as to get back the original salary ?

A) 39% B) 44% C) 56% D) 63%

Discuss

Answer & Solution

Answer: Option D

Solution:

Let original salary = Rs. 100
New salary :
90% of 85% of 80% of Rs. 100
$$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {\frac{{90}}{{100}} \times \frac{{85}}{{100}} \times \frac{{80}}{{100}} \times 100} \right) \cr & = {\text{Rs}}{\text{.}}\frac{{306}}{5} \cr} $$
Increase on $$\frac{{306}}{5}$$ :
= $$\left( {100 - \frac{{306}}{5}} \right)$$
= $$\frac{194}{5}$$
Increase on 100 :
$$\eqalign{ & = \left( {\frac{{194}}{5} \times \frac{5}{{306}} \times 100} \right)\% \cr & = \frac{{9700}}{{153}}\% . \cr & = 63.39 \approx 63\% \cr} $$

7

A building worth Rs. 133100 is constructed on land worth Rs. 72900. After how many years will the value of both be the same if land appreciates at 10% p.a. and building depreciates at 10% p.a. ?

A) $$1\frac{1}{2}$$ B) 2 C) $$2\frac{1}{2}$$ D) 3

Discuss

Answer & Solution

Answer: Option D

Solution:

Let the required time be n years
Then,
$$ \Leftrightarrow 72900 \times {\left( {1 + \frac{{10}}{{100}}} \right)^n} = $$ $$133100 \,\times $$ $${\left( {1 - \frac{{10}}{{100}}} \right)^n}$$
$$\eqalign{ & \Leftrightarrow {\left( {\frac{{11}}{{10}}} \right)^n} \times {\left( {\frac{{10}}{9}} \right)^n} = \frac{{133100}}{{72900}} \cr & \Leftrightarrow {\left( {\frac{{11}}{9}} \right)^n} = \frac{{1331}}{{729}} \cr & \Leftrightarrow {\left( {\frac{{11}}{9}} \right)^n} = {\left( {\frac{{11}}{9}} \right)^3} \cr & \Leftrightarrow n = 3 \cr} $$

8

A bag contains 600 coins of 25p denomination and 1200 coins of 50p denomination. If 12% of 25p coins and 24% of 50p are removed, the percentage of money removed from the bag is nearly :

A) 15.6% B) 17.8% C) 21.6% D) 30%

Discuss

Answer & Solution

Answer: Option C

Solution:

Total money :
$$\eqalign{ & = {\text{Rs}}{\text{. }}\left( {600 \times \frac{{25}}{{100}} + 1200 \times \frac{{50}}{{100}}} \right) \cr & = {\text{Rs}}{\text{. 750}} \cr} $$
25 paise coins removed :
$$\eqalign{ & = \left( {\frac{{12}}{{100}} \times 600} \right) \cr & = 72 \cr} $$
50 paise coins removed :
$$\eqalign{ & = \left( {\frac{{24}}{{100}} \times 1200} \right) \cr & = 288 \cr} $$
Money removed :
$$\eqalign{ & = {\text{Rs}}{\text{. }}\left( {72 \times \frac{{25}}{{100}} + 288 \times \frac{{50}}{{100}}} \right) \cr & = {\text{Rs}}{\text{. 162}} \cr} $$
∴ Required percentage :
$$\eqalign{ & = \left( {\frac{{162}}{{750}} \times 100} \right)\% \cr & = 21.6\% \cr} $$

9

Mr. More spent 20% of his monthly income on food and 15% on children's education. 40% of the remaining he spent on entertainment and transport together and 30% on medical. He is left with an amount of Rs. 8775 after all these expenditures. What is Mr. More's monthly income ?

A) Rs. 35000 B) Rs. 38000 C) Rs. 40000 D) Rs. 42000 E) None of these

Discuss

Answer & Solution

Answer: Option E

Solution:

Let Mr. More's monthly income be Rs. $$x$$
Then,
[100 - (40 + 30)]% of [100 - 20 + 15]% of $$x$$ = 8775
⇒ 30% of 65% of $$x$$ = 8775
⇒ $$\left( {\frac{{30}}{{100}} \times \frac{{65}}{{100}} \times x} \right)$$ = 8775
⇒ $$\frac{39}{200}$$ $$x$$ = 8775
⇒ $$x$$ = $$\left( {\frac{{8775 \times 200}}{{39}}} \right)$$
⇒ $$x$$ = 45000

10

If the price of erasers goes down by 25%, a man can buy 2 more erasers for a rupee. How many erasers are available for a rupee ?

A) 2 B) 4 C) 6 D) 8

Discuss

Answer & Solution

Answer: Option C

Solution:

Let the original price of an eraser be Rs. x
Reduced price = 75% of Rs. x = Rs. $$\frac{3x}{4}$$
$$\eqalign{ & \therefore \frac{1}{{\left( {\frac{{3x}}{4}} \right)}} - x = 2 \cr & \Rightarrow \frac{4}{{3x}} - \frac{1}{x} = 2 \cr & \Rightarrow \frac{1}{{3x}} = 2 \cr & \Rightarrow 6x = 1 \cr & \Rightarrow x = \frac{1}{6} \cr} $$
Hence, number of erasers available for a rupee = 6