Percentage - Aptitude MCQ Questions and Solutions with Explanations

41

If X is 20% less then Y, then find the value of $$\frac{Y - X}{Y}$$ and $$\frac{X}{X - Y}$$ :

A) $$\frac{1}{5}$$, - 4 B) 5, $$\frac{1}{4}$$ C) $$\frac{2}{5}$$, $$-\frac{5}{2}$$ D) $$\frac{3}{5}$$, $$-\frac{3}{5}$$

Discuss

Answer & Solution

Answer: Option A

Solution:

20% = $$\frac{1}{5}$$ = $$\frac{4}{5}$$
X : Y
4 : 5
Let X = 4a
Y = 5a
Hence,
⇔ $$\frac{Y - X}{Y}$$
= $$\frac{5a - 4a}{5a}$$
= $$\frac{a}{5a}$$
= $$\frac{1}{5}$$
⇔ $$\frac{X}{X - Y}$$
= $$\frac{4a}{4a - 5a}$$
= $$\frac{4a}{- a}$$
= - 4
Hence required answer = $$\frac{1}{5}$$, - 4

42

The ratio of the number of boys to that of girls in a school is 4 : 1. If 75% of boys and 70% of the girls are scholarship holders, then the percentage of students who do not get scholarship is :

A) 50% B) 28% C) 75% D) 26%

Discuss

Answer & Solution

Answer: Option D

Solution:

Let the number of boys = 400
Let the number of girls = 100
Total number of students who do not get scholarship
= 400 × $$\frac{25}{100}$$ + 100 × $$\frac{30}{100}$$
= 100 + 30
= 130
Required percentage
= $$\frac{130}{500}$$ × 100
= 26%

43

A man had a certain amount with him. He spent 20% of that to buy any article and 5% of the remaining on transport. Then he gifted Rs. 120. If he is left with Rs. 1400, the amount he spent on transport is :

A) Rs. 76 B) Rs. 61 C) Rs. 95 D) Rs. 80

Discuss

Answer & Solution

Answer: Option D

Solution:

Let the total amount = x
According to the question,
x × $$\frac{80}{100}$$ × $$\frac{95}{100}$$ = (120 + 1400)
x × $$\frac{4}{5}$$ × $$\frac{19}{20}$$ = 1520
x = $$\frac{1520 × 100}{76}$$
x = 2000
Total amount = 2000
Amount spent on transport
= 2000 × $$\frac{80}{100}$$ × $$\frac{5}{100}$$
= Rs. 80

44

The income of a company increases 20% per annum. If its income is Rs. 2664000 in the year 2012. Then its income in the year 2010 was :

A) Rs. 2120000 B) Rs. 1850000 C) Rs. 2820000 D) Rs. 2855000

Discuss

Answer & Solution

Answer: Option B

Solution:

Let the income in 2010 be P
⇒ R = 20%
⇒ Income of year 2012
⇒ Rs. 2664000
$$\eqalign{ & \Rightarrow {\text{Income of 2012}} = P{\left[ {1 + \frac{R}{{100}}} \right]^2} \cr & \Rightarrow 2664000 = P{\left[ {1 + \frac{{20}}{{100}}} \right]^2} \cr & \Rightarrow 2664000 = P \times \frac{6}{5} \times \frac{6}{5} \cr & \Rightarrow {\text{Income in 2010 = 1850000}} \cr} $$

45

An individual pays 30% income tax. On this he has to pay a surcharge of 10%. Thus, the net tax rate, he has pay is :

A) 45% B) 40% C) 33% D) 27%

Discuss

Answer & Solution

Answer: Option C

Solution:

Net tax rate
= 30 + $$\frac{30 × 10}{100}$$
= 33%

46

An army lost 10% of its men in war. 10% of the remaining died due to disease and 10% of the rest were declared disabled. Thus the strength of the army was reduced to 729000 active men. The original strength of the army was :

A) 1500000 B) 1000000 C) 1200000 D) 1100000

Discuss

Answer & Solution

Answer: Option B

Solution:

Initial number of soldiers in the army = x
According to the question,
$$\eqalign{ & \Rightarrow {\text{x}} \times \frac{{90}}{{100}} \times \frac{{90}}{{100}} \times \frac{{90}}{{100}} = 729000 \cr & \Rightarrow x = \frac{{729000 \times 1000}}{{9 \times 9 \times 9}} \cr & \Rightarrow x = 1000000 \cr} $$

Alternate:
10% → $$\frac{1}{10}$$
10 → 9 in war
10 → 9 in disease
10 → 9 disabled
100 → 729
729 → 729000
1 → 1000
10000 → 1000 × 1000 = 1000000

47

In an examination, 35% of total students failed in Hindi, 45% failed in English and 20% failed in both. Find the percentage of those students who passed in both the subjects ?

A) 45% B) 35% C) 20% D) 40%

Discuss

Answer & Solution

Answer: Option D

Solution:

Failed students in Hindi = 35%
Failed students in English = 45%
Student failed in both subject hindi and english = 20%
Student only fail in hind = 35 - 20 = 15%
Student only fail in English = 45 - 20 = 25%
Percentage of passed students in both subjects :
= 100 - [ student fail in hindi + student fail in english + student fail in both subject]
= [100 - (15 + 25 + 20)]
= 40%

48

The price of an article was increased by r%. Later the new price was decreased by r%. If the latest price was Rs. 1, then the original price was :

A) Rs. 1 B) Rs. $$\frac{{1 - {r^2}}}{{100}}$$ C) Rs. $$\frac{{\sqrt {1 - {r^2}} }}{{100}}$$ D) Rs. $$\left( {\frac{{10000}}{{10000 - {r^2}}}} \right)$$

Discuss

Answer & Solution

Answer: Option D

Solution:

r% = $$\frac{r}{100}$$

Initial Price		Final
100		(100 + r)
100		(100 - r)
10000		(100 + r) (100 - r)

According to the question,
(100 + r) (100 - r) units = Rs. 1
(10000 - r²) units = Rs. 1
1 unit = $$\left( {\frac{{1}}{{10000 - {r^2}}}} \right)$$
Original price = $$\left( {\frac{{10000}}{{10000 - {r^2}}}} \right)$$

49

The difference of two numbers is 15% of larger sum. The ratio of the larger number to the smaller number is :

A) 23 : 17 B) 11 : 9 C) 17 : 11 D) 23 : 11

Discuss

Answer & Solution

Answer: Option A

Solution:

Let the number are a and b
where a > b
According to the question,
(a - b) = $$\frac{15}{100}$$ (a + b)
(a - b) = $$\frac{3}{20}$$ (a + b)
20a - 20b = 3a + 3b
17a = 23b
$$\frac{a}{b}$$ = $$\frac{23}{17}$$
Required ratio = 23 : 17

50

A number if reduced by 25% becomes 225. By what percent should it be increased so that it becomes 375 ?

A) 25% B) 30% C) 35% D) 75%

Discuss

Answer & Solution

Answer: Option A

Solution:

Let the number = x
According to the question,
$$\frac{x × (100 - 25)}{100}$$ = 225
x = $$\frac{225 × 100}{75}$$
x = 300
Required percentage :
= $$\frac{(375 - 300)}{300}$$ × 100
= 25%