# Percentages Quiz Set 005

### Question 1

One number is 300 more than the other, and it is 75% of the sum of them. What is the number?

A

450.

B

550.

C

350.

D

650.

Soln.
Ans: a

Let the numbers be x and x - 300. We have been given x = \$75/100\$ × (x + x - 300), which gives 100x = 75 × (2x - 300), solving, we get x = 450.

### Question 2

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%

### Question 3

A clerk multiplied a number by 2/1 instead of 1/2. What is the percentage of error?

A

75 %.

B

77 %.

C

73 %.

D

79 %.

Soln.
Ans: a

If the actual figure is x, the error is \${2x}/1\$ - \${1x}/2\$ = \${2^2x - 1^2x}/{2 × 1}\$ = \${3x}/2\$, so %-error = \${(3x)/2}/{(2x)/1}\$ × 100 = \${3 × 1}/{2 × 2}\$ × 100 = 75%.

### Question 4

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 5

One number is 160 more than the other, and it is 70% of the sum of them. What is the number?

A

280.

B

380.

C

180.

D

480.

Soln.
Ans: a

Let the numbers be x and x - 160. We have been given x = \$70/100\$ × (x + x - 160), which gives 100x = 70 × (2x - 160), solving, we get x = 280.