Percentages Quiz Set 007

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Question 1

The sum of two numbers is 792. One of them is 164% of the other. The smaller number is?

 A

300.

 B

310.

 C

290.

 D

320.

Soln.
Ans: a

Let the numbers be x and ${164x}/100$. The sum is x + ${164x}/100$ which is same as ${264x}/100 = 792$. Solving we get the smaller number x = 300.


Question 2

In a sample there are 1260 items having a value of 50°C. 30% 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 - 30) = 70. If x is the size of the sample, 70% of x = 1260 + $2/3 × 1260$ = ${5 × 1260}/3$, which is same as ${70 × x}/100$ = ${5 × 1260}/3$. Solving, we get x = 3000.


Question 3

In a sample there are 750 items having a value of 50°C. 50% 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

2500 items.

 B

2510 items.

 C

2490 items.

 D

2520 items.

Soln.
Ans: a

The %age ≥ 50°C = (100 - 50) = 50. If x is the size of the sample, 50% of x = 750 + $2/3 × 750$ = ${5 × 750}/3$, which is same as ${50 × x}/100$ = ${5 × 750}/3$. Solving, we get x = 2500.


Question 4

In a sample there are 1620 items having a value of 50°C. 10% 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 - 10) = 90. If x is the size of the sample, 90% of x = 1620 + $2/3 × 1620$ = ${5 × 1620}/3$, which is same as ${90 × x}/100$ = ${5 × 1620}/3$. Solving, we get x = 3000.


Question 5

A number is first increased by 60%. By what percent must it be reduced so as to restore it to its previous value?

 A

$37{1/2}$ %.

 B

$38{1/2}$ %.

 C

$36{1/2}$ %.

 D

$20{1/4}$ %.

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 = ${100 × x}/{100 + x}$ = ${100 × 60}/{100 + 60}$ = ${75/2}$, which is same as: $37{1/2}$%.


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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 2017-05-17.

Posted by Parveen(Hoven),
Aptitude Trainer


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