# Percentages Quiz Set 017

### Question 1

A clerk multiplied a number by 5/1 instead of 1/5. What is the percentage of error?

A

96 %.

B

98 %.

C

94 %.

D

100 %.

Soln.
Ans: a

If the actual figure is x, the error is \${5x}/1\$ - \${1x}/5\$ = \${5^2x - 1^2x}/{5 × 1}\$ = \${24x}/5\$, so %-error = \${(24x)/5}/{(5x)/1}\$ × 100 = \${24 × 1}/{5 × 5}\$ × 100 = 96%.

### Question 2

The number of online customers increased from 1850 to 3975. What is the percentage increase?

A

\$114{32/37}\$ %.

B

\$119{1/12}\$ %.

C

\$108{1/39}\$ %.

D

\$111{32/39}\$ %.

Soln.
Ans: a

The increase is 3975 - 1850 = 2125. The percentage increase is \$2125/1850\$ × 100 = \${4250/37}\$, which is same as: \$114{32/37}\$.

### Question 3

If 11% of A + B = 18% of A - B, then what percent of B is A?

A

\$4{1/7}\$ %.

B

6 %.

C

\$2{4/9}\$ %.

D

\$5{5/9}\$ %.

Soln.
Ans: a

We have been given 11% of A + B = 18% of A - B, so \${A + B}/{A - B}\$ = \$18/11\$. By componendo and dividendo, \${(A + B) + (A - B)}/{(A + B) - (A - B)}\$ = \${18 + 11}/{18 - 11}\$, which gives \$A/B\$ = \$29/7\$ = \${29/7}\$, which is same as: \$4{1/7}\$%

### Question 4

Price of sugar is increased by 20%. By what percentage should consumption be reduced so that the expenditure remains same?

A

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

B

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

C

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

D

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

Soln.
Ans: a

Let price be Rs. 100/kg and the consumption be 1 kg. The current expenditure is 100 × 1 = Rs. 100. The new price of sugar is 100 + 20 = Rs. 120/kg. Let the new consumption be c kg. Now, if expenditure is to be same we should have 100 = 120 × c, which gives c = 100/120, so the decrease is 1 - \$100/120\$ = \${120 - 100}/120\$ × 100% = \${50/3}\$, which is same as: \$16{2/3}\$%.

### Question 5

If 17% of X + 8% of Y equals 2/3 of the sum of 4% of X and 15% of Y, then the ratio of X to Y is?

A

\${6/43}\$.

B

\$1{1/6}\$.

C

\$2{2/45}\$.

D

3.

Soln.
Ans: a

We can drop the % from both sides and write the given equation as 17X + 8Y = \$2/3\$ × (4X + 15Y), which is same as 3 × (17X + 8Y) = 2 × (4X + 15Y). Let r = X/Y. Dividing both sides by Y and putting r = X/Y, we get, 3 × (17r + 8) = 2 × (4r + 15), solving for r we get r = \${6/43}\$. 