# Percentages Quiz Set 002

### Question 1

The sum of two numbers is 1560. One of them is 160% of the other. The smaller number is?

A

600.

B

610.

C

590.

D

620.

Soln.
Ans: a

Let the numbers be x and \${160x}/100\$. The sum is x + \${160x}/100\$ which is same as \${260x}/100 = 1560\$. Solving we get the smaller number x = 600.

### Question 2

A number is first increased by 100%, and thereafter it is reduced by 100% again. What is the overall reduction?

A

100 %.

B

102 %.

C

98 %.

D

104 %.

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\$ = 100%

### Question 3

The number of online customers increased from 1075 to 2575. What is the percentage increase?

A

\$139{23/43}\$ %.

B

\$143{37/42}\$ %.

C

\$132{17/45}\$ %.

D

\$136{1/5}\$ %.

Soln.
Ans: a

The increase is 2575 - 1075 = 1500. The percentage increase is \$1500/1075\$ × 100 = \${6000/43}\$, which is same as: \$139{23/43}\$.

### Question 4

The age of Mr. X is 20% 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

\$16{2/3}\$ %.

B

\$26{1/2}\$ %.

C

\$15{2/3}\$ %.

D

\$11{4/5}\$ %.

Soln.
Ans: a

Age of Mr. X is 20 + \${20 × 20}/100\$ = 24 years. Mr. Y's age is less than Mr. X's age by \${20 × 20}/100\$ = 4 years. In terms of percentage, it is \$4/24\$ × 100 = \${50/3}\$, which is same as: \$16{2/3}\$.

### Question 5

A bag contains 280 red, 380 green and 1340 blue marbles. What percentage of the total is the most visible color in the bag?

A

67 %.

B

77 %.

C

57 %.

D

87 %.

Soln.
Ans: a

By inspection, blue is the most visible color. The percentage of blue is \$1340/{280 + 380 + 1340}\$ × 100 = 67%. 