# Percentages Quiz Set 004

### 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?

A

Rs. 800.

B

Rs. 810.

C

Rs. 790.

D

Rs. 820.

Soln.
Ans: a

Let the calls be for Rs. x. The total bill is x + 5% of x = \${21x}/20 = 840\$, which gives x = Rs. 800.

### 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%