Percentage practice test

1.

If 20% of a = b, then b% of 20 is the same as:

A. 4% of a
B. 5% of a
C. 20% of a
D. None of these

Answer: Option A
2.

A student divided a number by 2/3 when he required to multiply by 3/2. Calculate the percentage of error in his result.
A. 1
B. 0
C. 5
D. 3

Answer: Option B

Explanation:

Since 3x / 2 = x / (2 / 3)

3.

In a certain city only two newspapers A & B are published. It is known that 25% of the city population reads A & 20% read B while 8% read both A & B. It is also known that 30% of those who read A but not B, look into advertisements and 40% of those who read B but not A, look into advertisements while 50% of those who read both A & B look into advertisements. What % of the population reads an advertisement?

A. 12%
B. 13.2%
C. 13.9%
D. None of these

Answer: Option C

Explanation:

Let A & B denote sets of people who read paper A & paper B respectively and in all there are 100 people, then n(A) = 25, n(B) = 20, n (A ∩ B) = 8.
Hence the people who read paper A only i.e. n(A – B) = n (A) – n(A ∩ B) = 25 – 8 = 17.
And the people who read paper B only i.e. n(B – A) = n (B) – n (A ∩ B) = 20 – 8 = 12.
Now percentage of people reading an advertisement = [(30% of 17) + (40% of + 12) + (50% of 8)]% = 13.9 %.

4.

Vishal goes to a shop to buy a radio costing Rs 2568. The rate of sales tax is 7%. He tells the shopkeeper to reduce the price of the radio to such an extent that he has to pay Rs 2568, inclusive of all sales tax. Find the reduction needed in the price of the radio.

A. Rs 168
B. Rs 169
C. Rs 170
D. Rs 172

Answer: Option A

5.

In an election two candidates contested. A candidate secured 70% of the valid votes and is elected by a majority of 172 votes. Find the total number of valid votes.

A. 430
B. 570
C. 480
D. 520

Answer: Option A

Explanation:

Let the total number of valid votes be ‘x’

70% of x = 70/100 *x = 7x/10

Number of votes secured by the other candidate = x-7x/10 = 3x/10

Given, 7x/10-3x/10 = 172

4x/10 = 172

4x = 1720

x = 1720/4 = 430

6.

The percentage increases of population for three consecutive years in a country are 10%, 25% and 10% respectively. What is the total percentage increase for the three years?

A. 45%
B. 42.5%
C. 41.25%
D. 51.25%

Answer: Option D

Explanation:

Let us assume the initial population as 100.
Population at the end of first year=10% increase on 100=110
Population at the end of second year=25% increase on 110= 25/100 X110=137.5
Population at the end of third year=10% increase on 137.5= 10/100 X137.5=151.25
Therefore the population has increased from 100 to 151.25 in 3 years.
Since our initial population is 100, we can directly take the percentage increase as 51.25%

7.

A 5 litre jug contains 4 litres of a salt water solution that is 15 percent salt. If 1.5 litres of the solution spills out of the jug, and the jug is then filled to capacity with water, approximately what percent of the resulting solution in the jug is salt?

A. 9.5%
B. 7.5%
C. 10.5%
D. 12%

Answer: Option B

8.

In a certain department store, which has four sizes of a specific shirt, there are 1/3 as many small shirts as medium shirts, and 1/2 as many large shirts as small shirts. If there are as many x-large shirts as large shirts, what percent of the shirts in the store are medium?

A. 25%
B.  33%
C. 50%
D. 60%

Answer: Option D

Explanation:

total shirts are 1 part
1/3M+m+1/6m+1/6m=1
5/3m=1
m=3/5*100
so m=60%

9.

Each side of a rectangle is increased by 100% .By what percentage does the area increase?

A. 200
B. 300
C. 250
D. 350
Answer: Option B

Explanation:

Let assume the length and bridth of rectangle are x and y.
Now,The area is xy.
When it is increased by 100%,the new length and bridth are 2x,2y.
Now,the area is 4xy.
So,the area increased 300%

10.

Aman won a competition and so he got some prize money. He gave Rs. 2000 less than the half of prize money to his son and Rs. 1000 more than the two third of the remaining to his daughter. If both they got same amount, what is the prize money Aman got?

A. 25000
B. 26000
C. 27000
D. None of these

Answer: Option B

Explanation:

Assume Aman got x rupees.
He gave x/2 – 2000 to his son.
And 2/3 ( x/2 + 2000 ) + 1000 to his daughter.
x/2 – 2000 = x/3 + 7000/3
x = 26000