# Percentages Quiz Set 020

### Question 1

If 5% of X + 4% of Y equals 2/3 of the sum of 3% of X and 16% of Y, then the ratio of X to Y is?

A

\$2{2/9}\$.

B

\$3{5/8}\$.

C

1.

D

\$4{3/11}\$.

Soln.
Ans: a

We can drop the % from both sides and write the given equation as 5X + 4Y = \$2/3\$ × (3X + 16Y), which is same as 3 × (5X + 4Y) = 2 × (3X + 16Y). Let r = X/Y. Dividing both sides by Y and putting r = X/Y, we get, 3 × (5r + 4) = 2 × (3r + 16), solving for r we get r = \${20/9}\$, which is same as: \$2{2/9}\$.

### Question 2

If 11% of X + 7% of Y equals 2/3 of the sum of 6% of X and 13% of Y, then the ratio of X to Y is?

A

\${5/21}\$.

B

\$1{3/10}\$.

C

\$2{1/23}\$.

D

\$2{22/23}\$.

Soln.
Ans: a

We can drop the % from both sides and write the given equation as 11X + 7Y = \$2/3\$ × (6X + 13Y), which is same as 3 × (11X + 7Y) = 2 × (6X + 13Y). Let r = X/Y. Dividing both sides by Y and putting r = X/Y, we get, 3 × (11r + 7) = 2 × (6r + 13), solving for r we get r = \${5/21}\$.

### Question 3

Two numbers are, respectively, 15% and 50% less than a third number. What percent is the second of the first?

A

\$58{14/17}\$ %.

B

\$63{9/16}\$ %.

C

\$51{14/19}\$ %.

D

\$55{6/19}\$ %.

Soln.
Ans: a

If the third number is 100, first number is (100 - 15) = 85, and the second number is (100 - 50) = 50. The required ratio is \$50/85\$ × 100 = \${1000/17}\$, which is same as: \$58{14/17}\$%.

### Question 4

A sample of alcohol has 40% water, and another sample has 60% water. If equal volumes of both the samples are combined, what is the percentage of water in the new sample?

A

50 %.

B

52 %.

C

48 %.

D

54 %.

Soln.
Ans: a

If 100 units of both alcohol are combined, there will be 100 units of water in 200 units of the new sample. The percentage of water is \$100/200\$ × 100 = 50%.

### Question 5

If 58 is m% of p, and B is p% of m, then what is B?

A

58.

B

68.

C

48.

D

78.

Soln.
Ans: a

Let 58 = A, so A = \$m/100\$ × p = \$p/100\$ × m. = B, so A and B are same. 