Percentage - Aptitude MCQ Questions and Solutions with Explanations

61

Two numbers A and B such that the sum of 5% of A and 4% of B is $$\frac{2}{3}$$rd of the sum of 6% of A and 8% of B. The ratio A : B is -

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

Discuss

Answer & Solution

Answer: Option A

Solution:

According to the question,
$$\eqalign{ & \frac{5}{{100}}A + \frac{4}{{100}}B = \frac{2}{3}\left[ {\frac{{6A}}{{100}} + \frac{{8B}}{{100}}} \right] \cr & \Rightarrow 5A + 4B = \frac{2}{3}\left( {6A + 8B} \right) \cr & \Rightarrow 15A + 12B = 12A + 16B \cr & \Rightarrow 3A = 4B \cr & \Rightarrow \frac{A}{B} = \frac{4}{3} \cr & \Rightarrow A:B = 4:3 \cr} $$

62

If a number is increased by 25% and the resulting number is decreased by 25%, then the percentage increase or decrease finally is :

A) No change B) Decreased by $$6\frac{1}{4}$$% C) Increased by $$6\frac{1}{4}$$% D) Increased by 6%

Discuss

Answer & Solution

Answer: Option B

Solution:

Required % decrements :
$$\eqalign{ & = \frac{{{x^2}}}{{100}}\% \cr & = \frac{{{{\left( {25} \right)}^2}}}{{100}} \cr & = 6\frac{1}{4}\% \cr} $$

63

In an examination, 60% of the candidates passed in English and 70% of the candidates passed in Mathematics, but 20% failed in both subjects. If 2500 candidates passed in both the subjects, the number of candidates who appeared at the examination was :

A) 3000 B) 3500 C) 4000 D) 5000

Discuss

Answer & Solution

Answer: Option D

Solution:

Candidates failed in English
= (100 - 60)%
= 40%
Candidate failed in Mathematics
= (100 - 70)%
= 30%
20% Candidate fail in Both.
Candidate only fail in English = 40 - 20 = 20%
Candidate only fail in Mathematics = 30 - 20 = 10%
Students passed in both subjects
= 100 - (20% Candidate fail in Both + Candidate only fail in English + Candidate only fail in Mathematics)
= 100 - (20 + 20 + 10)
= 50%
50% of students = 2500
Total students = $$\frac{{2500}}{{50}} \times 100$$
= 5000

64

The value of a property depreciates every year by 10% of its value at the beginning of the year. The present value of the property is Rs. 8100. What was its value 2 years ago ?

A) Rs. 10000 B) Rs. $${\left( {\frac{{90}}{{11}}} \right)^2} \times 100$$ C) Rs. $${\left( {\frac{{100}}{{101}}} \right)^2} \times 8100$$ D) Rs. 9801

Discuss

Answer & Solution

Answer: Option A

Solution:

10% = $$\frac{1}{10}$$
\[\begin{gathered} {\text{Initial }}\,\,\,\,\,\,{\text{Final}} \hfill \\ \,\,\,{\text{10}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,9 \hfill \\ \,\,\,10\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,9 \hfill \\ \overline {\,\,100\,\,\,\,\,\,\,\,\,\,\,\,\,81\,\,\,} \hfill \\ \end{gathered} \]
⇒ 81 units = Rs. 8100
⇒ 1 unit = Rs. 100
⇒ 100 units = Rs. 10000
⇒ Value of property 2 years ago
⇒ Rs. 10000

65

If a man receives on one-fourth of his capital 3% interest, on two third 5% and one the remaining 11%, the percentage interest he receives on the whole is :

A) 4.5% B) 5% C) 5.5% D) 5.2%

Discuss

Answer & Solution

Answer: Option B

Solution:

Let the total capital = 1200
According to the question,
one-fourth of 1200 = 300, two third of 1200 = 800, remain 100
Interest on 300 = 3% of 300 = 9
Interest on 800 = 5% of 800 = 40
Interest on 100 = 11% of 100 = 11
Total interest = (9 + 40 + 11) = 60
Required percentage :
= $$\frac{60}{1200}$$ × 100
= 5%

66

The difference between the value of the number increased by 20% and the value of the number decreased by 25% is 36. Find the number ?

A) 7.2 B) 0.8 C) 720 D) 80

Discuss

Answer & Solution

Answer: Option D

Solution:

Let the number = x
According to the question,
⇒ x × $$\frac{120}{100}$$ - x × $$\frac{75}{100}$$ = 36
⇒ 120x - 75x = 3600
⇒ 45x = 3600
⇒ x = $$\frac{3600}{45}$$
⇒ x = 80
Hence, required number = 80

67

In a village, each of the 60% of families has a cow; each of the 30% of families has a buffalo and each of the 15% of families has both a cow and buffalo. In all there are 96 families in the village. How many families do not have a cow or a buffalo ?

A) 20 B) 24 C) 26 D) 28

Discuss

Answer & Solution

Answer: Option B

Solution:

15% of families have cow and buffalo.
Families only have cow = 60 - 15 = 45%
Families only have buffalo = 30 - 15 = 15%
Required families which do not have a cow or a buffalo
= 100 - (Families only have cow + Families only have buffalo + Families have cow and buffalo)
= 100 - (45 + 15 + 15)
= 25%
According to the question,
Required number
= $$\frac{96}{100}$$ × 25
= 24

68

The population of a village has increased annually at the rate of 25%. If at the end of 3 years it is 10000, the population in the beginning of the first year was :

A) 5120 B) 5000 C) 4900 D) 4500

Discuss

Answer & Solution

Answer: Option A

Solution:

25% = $$\frac{1}{4}$$
\[\begin{gathered} {\text{Initial }}\,\,\,\,\,\,{\text{Final}} \hfill \\ \,\,\,4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,5 \hfill \\ \,\,\,4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,5 \hfill \\ \,\,\,4\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,5 \hfill \\ \overline {\,\,\,\,\,\,64\,\,\,\,\,\,\,\,\,\,125\,\,\,} \hfill \\ \end{gathered} \]

⇒ 125 units = 10000
⇒ 1 unit = 80
⇒ 64 units = 5120
⇒ Population at the beginning of 1^st year = 5120

69

A saves 20% of his monthly salary. If his monthly expenditure is Rs. 6000, then his monthly savings is :

A) Rs. 1500 B) Rs. 1800 C) Rs. 1200 D) Rs. 4800

Discuss

Answer & Solution

Answer: Option A

Solution:

Let the salary = 100 units
Savings = 20%
Savings = 100 × $$\frac{20}{100}$$ = 20 units
Expenditure = (100 - 20) = 80 units
According to the question,
80 units = Rs. 6000
1 unit = Rs. 75
Savings = 75 × 20 = Rs. 1500

70

A man spends 75% of his income. His income increased by 20% and he increased his expenditure by 15%. His savings will then be increased by :

A) 33% B) $$33\frac{1}{3}$$% C) 35% D) 40%

Discuss

Answer & Solution

Answer: Option C

Solution:

Let the income of the man = Rs. 100
∴Intial Expenditure = Rs.75
Now new income become = 100 + 20% of 100 = Rs. 120
New Expenditure = 75 + 15% of 75 = Rs.86.25
Intial Saving = 100 - 75 = Rs. 25
New Saving = 120 - 86.25 = Rs. 33.75
Required percentage increase :
= $$\frac{(33.75 - 25)}{25}$$ × 100
= 35%