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### Question 1

A number is first increased by 100%. By what percent must it be reduced so as to restore it to its previous value?

**A**

50 %.

**B**

51 %.

**C**

49 %.

**D**

$17{2/3}$ %.

**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 = ${100 × x}/{100 + x}$ = ${100 × 100}/{100 + 100}$ = 50%.

### Question 2

Price of sugar is increased by 60%. By what percentage should consumption be reduced so that the expenditure remains same?

**A**

$37{1/2}$ %.

**B**

$38{1/2}$ %.

**C**

$36{1/2}$ %.

**D**

$20{1/4}$ %.

**Soln.**

**Ans: a**

Let price be Rs. 100/kg and the consumption be 1 kg. The current expenditure is 100 × 1 = Rs. 100. The new price of sugar is 100 + 60 = Rs. 160/kg. Let the new consumption be c kg. Now, if expenditure is to be same we should have 100 = 160 × c, which gives c = 100/160, so the decrease is 1 - $100/160$ = ${160 - 100}/160$ × 100% = ${75/2}$, which is same as: $37{1/2}$%.

### Question 3

Price of sugar is increased by 80%. By what percentage should consumption be reduced so that the expenditure remains same?

**A**

$44{4/9}$ %.

**B**

$51{1/8}$ %.

**C**

$35{6/11}$ %.

**D**

$38{9/11}$ %.

**Soln.**

**Ans: a**

Let price be Rs. 100/kg and the consumption be 1 kg. The current expenditure is 100 × 1 = Rs. 100. The new price of sugar is 100 + 80 = Rs. 180/kg. Let the new consumption be c kg. Now, if expenditure is to be same we should have 100 = 180 × c, which gives c = 100/180, so the decrease is 1 - $100/180$ = ${180 - 100}/180$ × 100% = ${400/9}$, which is same as: $44{4/9}$%.

### Question 4

The age of Mr. X is 60% more than Mr. Y's age which is 20 years at present. By what percent is Y's age less than Mr. X's age?

**A**

$37{1/2}$ %.

**B**

$38{1/2}$ %.

**C**

$36{1/2}$ %.

**D**

$20{1/4}$ %.

**Soln.**

**Ans: a**

Age of Mr. X is 20 + ${60 × 20}/100$ = 32 years. Mr. Y's age is less than Mr. X's age by ${60 × 20}/100$ = 12 years. In terms of percentage, it is $12/32$ × 100 = ${75/2}$, which is same as: $37{1/2}$.

### Question 5

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?

This Blog Post/Article "Percentages Quiz Set 012" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2019-08-18.