Percentages Quiz Set 007

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Question 1

If 9% of X + 2% of Y equals 2/3 of the sum of 8% of X and 7% of Y, then the ratio of X to Y is?

 A

${8/11}$.

 B

$1{9/10}$.

 C

$2{4/13}$.

 D

$3{2/13}$.

Soln.
Ans: a

We can drop the % from both sides and write the given equation as 9X + 2Y = $2/3$ × (8X + 7Y), which is same as 3 × (9X + 2Y) = 2 × (8X + 7Y). Let r = X/Y. Dividing both sides by Y and putting r = X/Y, we get, 3 × (9r + 2) = 2 × (8r + 7), solving for r we get r = ${8/11}$.


Question 2

In a sample there are 1440 items having a value of 50°C. 20% values are below 50°C, and the number of values above 50°C is $2/3$ of the items having a value of 50°C. What is the size of the sample?

 A

3000 items.

 B

3010 items.

 C

2990 items.

 D

3020 items.

Soln.
Ans: a

The %age ≥ 50°C = (100 - 20) = 80. If x is the size of the sample, 80% of x = 1440 + $2/3 × 1440$ = ${5 × 1440}/3$, which is same as ${80 × x}/100$ = ${5 × 1440}/3$. Solving, we get x = 3000.


Question 3

If 85 is m% of p, and B is p% of m, then what is B?

 A

85.

 B

95.

 C

75.

 D

105.

Soln.
Ans: a

Let 85 = A, so A = $m/100$ × p = $p/100$ × m. = B, so A and B are same.


Question 4

A number is first increased by 20%. By what percent must it be reduced so as to restore it to its previous value?

 A

$16{2/3}$ %.

 B

$26{1/2}$ %.

 C

$15{2/3}$ %.

 D

$11{4/5}$ %.

Soln.
Ans: a

Let us derive the shortcut formula first, so that you can remember it and use it when the need arises. Suppose the number is 100, and let the increase be x%. The number becomes 100 + x. Let us suppose that it has to be reduced by p% to restore it to 100. Then, (100 + x) - p × $(100 + x)/100$ = 100. We can cancel away 100, and easily simplify it to p = ${100 × x}/{100 + x}$ = ${100 × 20}/{100 + 20}$ = ${50/3}$, which is same as: $16{2/3}$%.


Question 5

One number is 76 more than the other, and it is 69% of the sum of them. What is the number?

 A

138.

 B

238.

 C

438.

 D

338.

Soln.
Ans: a

Let the numbers be x and x - 76. We have been given x = $69/100$ × (x + x - 76), which gives 100x = 69 × (2x - 76), solving, we get x = 138.


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Creative Commons License
This Blog Post/Article "Percentages Quiz Set 007" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-10-26.

Posted by Parveen(Hoven),
Aptitude Trainer


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