# Percentages Quiz Set 001

### Question 1

If 82 is m% of p, and B is p% of m, then what is B?

A

82.

B

92.

C

72.

D

102.

Soln.
Ans: a

Let 82 = A, so A = \$m/100\$ × p = \$p/100\$ × m. = B, so A and B are same.

### Question 2

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 3

If 20% of X is Y, then Y% of 20 is?

A

4 % of X.

B

14 % of X.

C

34 % of X.

D

24 % of X.

Soln.
Ans: a

We have Y = \$(20 × X)/100\$, so Y% of 20 is same as \$(20 × X)/100\$% × 20, which can be rearranged to \$(20 × 20)/100\$% × X = 4% of X.

### Question 4

A carton contains 3000 led bulbs, some of them are red, some green and others are blue. How many are green if 9% are red and 5% are blue?

A

2580.

B

2680.

C

2480.

D

2780.

Soln.
Ans: a

The percentage of green is 100 - (9 + 5) = 86. So number of green bulbs = \$86/100\$ × 3000 = 2580.

### Question 5

A number is first increased by 80%. By what percent must it be reduced so as to restore it to its previous value?

A

\$44{4/9}\$ %.

B

\$51{1/8}\$ %.

C

\$35{6/11}\$ %.

D

\$38{9/11}\$ %.

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 × 80}/{100 + 80}\$ = \${400/9}\$, which is same as: \$44{4/9}\$%. 