# Percentages Quiz Set 001

### Question 1

If 7% of A + B = 11% of A - B, then what percent of B is A?

A

\$4{1/2}\$ %.

B

\$5{1/2}\$ %.

C

\$3{1/2}\$ %.

D

\$3{3/4}\$ %.

Soln.
Ans: a

We have been given 7% of A + B = 11% of A - B, so \${A + B}/{A - B}\$ = \$11/7\$. By componendo and dividendo, \${(A + B) + (A - B)}/{(A + B) - (A - B)}\$ = \${11 + 7}/{11 - 7}\$, which gives \$A/B\$ = \$18/4\$ = \${9/2}\$, which is same as: \$4{1/2}\$%

### 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

A number is first increased by 60%, and thereafter it is reduced by 60% again. What is the overall reduction?

A

36 %.

B

38 %.

C

34 %.

D

40 %.

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\$ = 36%

### Question 4

The number of online customers increased from 625 to 2075. What is the percentage increase?

A

232 %.

B

233 %.

C

231 %.

D

\$78{1/3}\$ %.

Soln.
Ans: a

The increase is 2075 - 625 = 1450. The percentage increase is \$1450/625\$ × 100 = 232.

### Question 5

If 4% of A + B = 9% of A - B, then what percent of B is A?

A

\$2{3/5}\$ %.

B

\$4{1/2}\$ %.

C

\$1{1/7}\$ %.

D

4 %.

Soln.
Ans: a

We have been given 4% of A + B = 9% of A - B, so \${A + B}/{A - B}\$ = \$9/4\$. By componendo and dividendo, \${(A + B) + (A - B)}/{(A + B) - (A - B)}\$ = \${9 + 4}/{9 - 4}\$, which gives \$A/B\$ = \$13/5\$ = \${13/5}\$, which is same as: \$2{3/5}\$%