Percentage - Aptitude MCQ Questions and Solutions with Explanations

21

In an election between two candidates, 85% of the voters cast their votes, out which 4% of the votes were declared invalid. A candidate got 6936 votes which were 85% of the valid votes. Find the total number of voters enrolled in that election.

A) 10,700 B) 10,500 C) 10,800 D) 10,000

Discuss

Answer & Solution

Answer: Option D

Solution:

$$\eqalign{ & 72.25\mu \to 6936 \cr & 100\mu \to \frac{{6936 \times 100}}{{72.25}} \cr & 100\mu \to 9600 \cr & \Rightarrow {\text{Valid votes }}96\mu \to 9600 \cr & 1\mu \to 100 \cr & 100\mu \to 10000{\text{ Answer}} \cr} $$

22

In an election between two candidates, 5% of the registered voters did not cast their vote. 10% of the votes were found to be either invalid or of NOTA. The winning candidate received 60% votes in his favour and won the election by 17271 votes. Find the number of registered voters.

A) 90252 B) 100000 C) 101000 D) 102500

Discuss

Answer & Solution

Answer: Option C

Solution:

$$\eqalign{ & 20\% {\text{ of }}885 = 17271 \cr & 855 \times \frac{{20}}{{100}} = 17271 \cr & 1 \to 101 \cr & \therefore 1000 = 101000 \cr} $$

23

ln an examination, the number of students who passed and the number of students who failed were in the ratio 25 : 4. If one more students had appeared and passed and the number of failed students was 3 less than earlier, the ratio of passed students to failed students would have become 22 : 3. What is the difference between the number of students who, initially, passed the examination and the number of students who failed the examination?

A) 132 B) 174 C) 126 D) 150

Discuss

Answer & Solution

Answer: Option C

Solution:

Ratio of passed student to fails students = Pass : Fail = 25x : 4x
Total number 25x + 4x = 29x
New ratio of passed student to fails students = Pass : Fail = 22x : 3x = 25x
$$\frac{{{\text{Fail}}}}{{{\text{Total}}}} = \frac{{4x - 3}}{{29x + 1}} = \frac{3}{{25}}$$
100x - 75 = 87x + 3
13x = 78
x = 6
So, the difference is = 25x - 4x
= 21x
= 21 × 6
= 126

24

Anuja owns $$66\frac{2}{3}\% $$ of a property. If 30% of the property that she owns is worth Rs. 1,25,000, then 45% of the value (in Rs.) of the property is:

A) 2,70,000 B) 2,81,250 C) 2,25,000 D) 2,62,500

Discuss

Answer & Solution

Answer: Option B

Solution:

$$\eqalign{ & {\text{Let the property}} = 300\,{\text{units}} \cr & {\text{Anuja have}} = 300 \times \frac{2}{3} = 200{\text{ units}} \cr & \frac{{200 \times 30}}{{100}} \to 125000 \cr & 60{\text{ units}} \to {\text{125000}} \cr & {\text{1 unit}} \to \frac{{12500}}{6} \cr & 95\% {\text{ of }}300 = 135 \cr & 135{\text{ units}} \to {\text{135}} \times \frac{{12500}}{6} \cr & = 45 \times 6250 \cr & = {\text{Rs}}{\text{. }}281250 \cr} $$

25

Ankita's weight is 20% less than that of her grandmother. The grandmother weights 26 kg less than grandmother's husband, whose weight is 81 kg. If Ankita's brother is 8 kg heavier than Ankita, then what is the weight (in kg) of Ankita's brother?

A) 60 B) 19 C) 36 D) 52

Discuss

Answer & Solution

Answer: Option D

Solution:

Grand mother's husband's, weight = 81 kg
Grand mother's weight = (81 - 26) kg = 55 kg
20% = $$\frac{1}{5}$$
Ankita's weight = 55 × $$\frac{4}{5}$$ = 44 kg
Ankita's brother's weight = 44 + 8 = 52 kg

26

If each side of a square is decreased by 17%, then by what percentage does its area decrease?

A) 30.79% B) 31.11% C) 25% D) 44.31%

Discuss

Answer & Solution

Answer: Option B

Solution:

$$ = \frac{{3111 \times 100}}{{10000}} = 31.11\% $$

27

The volume of the water in two tanks, A and B, is in the ratio of 6 : 5. The volume of water in tank A is increased by 30%. By what percentage should the volume of water in tank B be increased so that both the tanks have the same volume of water?

A) 56% B) 18% C) 15% D) 30%

Discuss

Answer & Solution

Answer: Option A

Solution:

A : B = 6 : 5
Let A = 600, B = 500
After 30% increased A = 780
We have to increase = 280
Increase% $$ = \frac{{280}}{{500}} \times 100 = 56\% $$

28

The monthly salary of a person was Rs. 1,60,000. He used to spend on three heads Personal and family expenses (P), Taxes (T) and Education loan (E). The rest were his savings. P was 50% of the income, E was 20% of P and T was 15% of E. When his salary got raised by 30%, he maintained the percentage level of P, but E became 30% of P and T became 20% of E. The sum of the two savings (in Rs.) is:

A) 2,11,680 B) 1,28,160 C) 1,18,000 D) 1,62,810

Discuss

Answer & Solution

Answer: Option B

Solution:

Salary = Rs. 160000
Personal and family expenses (P) = 50% of 160000 = 80000
Education loan (E) = 20% of 80000 = 16000
Taxes (T) = 15% of 16000 = 2400
Saving = 160000 - 80000 - 16000 - 2400 = 61600
New salary = 130% of 160000 = Rs. 208000
Personal and family expenses (P) = 50% of 208000 = 104000
Education loan (E) = 30% of 104000 = 31200
Taxes (T) = 20% of 31200 = 6240
Saving = 208000 - 104000 - 31200 - 6240 = 66560
Sum of the two saving = 61600 + 66560 = 128160

29

The number of students in a class is 45, out of which $$33\frac{1}{3}\% $$ are boys and the rest are girls. The average score of girls is Science is $$66\frac{2}{3}\% $$ more than that of boys. If the average score of all the students is 78, then the average score of girls is:

A) 54 B) 65 C) 78 D) 90

Discuss

Answer & Solution

Answer: Option D

Solution:

Number of students = 45
Number of boys = $$33\frac{1}{3}\% $$ of 45 = 15
Number of girls = 45 - 15 = 30
Obtain marks of girls in science subject is $$66\frac{2}{3}\% $$ more then the obtain marks of boys.
$$\eqalign{ & 66\frac{2}{3}\% = \frac{2}{3} \cr & \frac{{{\text{Girls}}}}{{{\text{Boys}}}} = \frac{{5x}}{{3x}} \cr} $$
Total marks
15 × 3x + 30 × 5x = 45 × 78
3x + 2 × 5x = 3 × 78
13x = 3 × 78
x = 3 × 6
x = 18
5x = 18 × 5
5x = 90

30

A saves 35% of his income. If his income increase by 20.1% and his expenditure increase by 20%, then by what percentage do his saving increase or decrease? (correct to one decimal place)

A) 20.3% of increase B) 18.5% of decrease C) 19.75% of decrease D) 21.9% of increase

Discuss

Answer & Solution

Answer: Option A

Solution:

\[\begin{array}{l} 35\% = \frac{{35}}{{100}}\\ {\rm{Income}} = 100\\ {\rm{Saving}} = 35\\ {\rm{Expenditure}} = 65\\ \begin{array}{*{20}{c}} {{\rm{Income}}}& = &{{\rm{Expenditure}}}& + &{{\rm{Saving}}}\\ {100}& = &{65}& + &{35}\\ {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \downarrow + 20.1}&{}&{\,\,\,\,\,\,\,\,\,\,\,\,\, \downarrow + 20}&{}&{}\\ {120.1}& = &{78}& + &x \end{array}\\ x = 120.1 - 78 = 42.1\\ {\rm{Increase \,in \,saving}} = 42.1 - 35 = 7.1\\ {\rm{Increase }}\% = \frac{{7.1}}{{35}} \times 100 = 20.3\% \end{array}\]