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### Question 1

If 3% of A + B = 11% of A - B, then what percent of B is A?

**A**

$1{3/4}$ %.

**B**

$3{2/3}$ %.

**C**

${1/2}$ %.

**D**

$3{1/6}$ %.

**Soln.**

**Ans: a**

We have been given 3% of A + B = 11% of A - B, so ${A + B}/{A - B}$ = $11/3$. By componendo and dividendo, ${(A + B) + (A - B)}/{(A + B) - (A - B)}$ = ${11 + 3}/{11 - 3}$, which gives $A/B$ = $14/8$ = ${7/4}$, which is same as: $1{3/4}$%

### Question 2

The age of Mr. X is 80% 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**

$44{4/9}$ %.

**B**

$51{1/8}$ %.

**C**

$35{6/11}$ %.

**D**

$38{9/11}$ %.

**Soln.**

**Ans: a**

Age of Mr. X is 20 + ${80 × 20}/100$ = 36 years. Mr. Y's age is less than Mr. X's age by ${80 × 20}/100$ = 16 years. In terms of percentage, it is $16/36$ × 100 = ${400/9}$, which is same as: $44{4/9}$.

### Question 3

The age of Mr. X is 40% 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**

$28{4/7}$ %.

**B**

$34{1/2}$ %.

**C**

$21{4/9}$ %.

**D**

$24{5/9}$ %.

**Soln.**

**Ans: a**

Age of Mr. X is 20 + ${40 × 20}/100$ = 28 years. Mr. Y's age is less than Mr. X's age by ${40 × 20}/100$ = 8 years. In terms of percentage, it is $8/28$ × 100 = ${200/7}$, which is same as: $28{4/7}$.

### Question 4

The service tax is 5%. A person receives a telephone bill amounting to Rs. 840. How much was the bill excluding tax?

### Question 5

A number is first increased by 20%, and thereafter it is reduced by 20% again. What is the overall reduction?

**A**

4 %.

**B**

6 %.

**C**

10 %.

**D**

8 %.

**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. When it is reduced by x%, we get 100 + x - $((100 + x) × x)/100$ = 100 + x - $(x + x^2/100)$ = 100 - $x^2/100$, hence a reduction of $x^2/100$ = 4%

### More Chapters | See All...

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This Blog Post/Article "Percentages Quiz Set 004" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2017-10-26.