# Percentages Quiz Set 006

### Question 1

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 2

Price of sugar is increased by 100%. By what percentage should consumption be reduced so that the expenditure remains same?

A

50 %.

B

51 %.

C

49 %.

D

\$17{2/3}\$ %.

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 + 100 = Rs. 200/kg. Let the new consumption be c kg. Now, if expenditure is to be same we should have 100 = 200 × c, which gives c = 100/200, so the decrease is 1 - \$100/200\$ = \${200 - 100}/200\$ × 100% = 50%.

### Question 3

If 13% of X + 2% of Y equals 2/3 of the sum of 11% of X and 15% of Y, then the ratio of X to Y is?

A

\$1{7/17}\$.

B

\$2{9/16}\$.

C

\${7/19}\$.

D

\$3{18/19}\$.

Soln.
Ans: a

We can drop the % from both sides and write the given equation as 13X + 2Y = \$2/3\$ × (11X + 15Y), which is same as 3 × (13X + 2Y) = 2 × (11X + 15Y). Let r = X/Y. Dividing both sides by Y and putting r = X/Y, we get, 3 × (13r + 2) = 2 × (11r + 15), solving for r we get r = \${24/17}\$, which is same as: \$1{7/17}\$.

### Question 4

Two numbers are, respectively, 5% and 25% less than a third number. What percent is the second of the first?

A

\$78{18/19}\$ %.

B

\$84{7/18}\$ %.

C

\$70{11/21}\$ %.

D

\$74{1/7}\$ %.

Soln.
Ans: a

If the third number is 100, first number is (100 - 5) = 95, and the second number is (100 - 25) = 75. The required ratio is \$75/95\$ × 100 = \${1500/19}\$, which is same as: \$78{18/19}\$%.

### Question 5

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}\$.