# Percentages Quiz Set 007

### Question 1

If 9% of X + 2% of Y equals 2/3 of the sum of 8% of X and 7% of Y, then the ratio of X to Y is?

A

\${8/11}\$.

B

\$1{9/10}\$.

C

\$2{4/13}\$.

D

\$3{2/13}\$.

Soln.
Ans: a

We can drop the % from both sides and write the given equation as 9X + 2Y = \$2/3\$ × (8X + 7Y), which is same as 3 × (9X + 2Y) = 2 × (8X + 7Y). Let r = X/Y. Dividing both sides by Y and putting r = X/Y, we get, 3 × (9r + 2) = 2 × (8r + 7), solving for r we get r = \${8/11}\$.

### Question 2

In a sample there are 1440 items having a value of 50°C. 20% values are below 50°C, and the number of values above 50°C is \$2/3\$ of the items having a value of 50°C. What is the size of the sample?

A

3000 items.

B

3010 items.

C

2990 items.

D

3020 items.

Soln.
Ans: a

The %age ≥ 50°C = (100 - 20) = 80. If x is the size of the sample, 80% of x = 1440 + \$2/3 × 1440\$ = \${5 × 1440}/3\$, which is same as \${80 × x}/100\$ = \${5 × 1440}/3\$. Solving, we get x = 3000.

### Question 3

If 85 is m% of p, and B is p% of m, then what is B?

A

85.

B

95.

C

75.

D

105.

Soln.
Ans: a

Let 85 = A, so A = \$m/100\$ × p = \$p/100\$ × m. = B, so A and B are same.

### Question 4

A number is first increased by 20%. By what percent must it be reduced so as to restore it to its previous value?

A

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

B

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

C

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

D

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

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. Let us suppose that it has to be reduced by p% to restore it to 100. Then, (100 + x) - p × \$(100 + x)/100\$ = 100. We can cancel away 100, and easily simplify it to p = \${100 × x}/{100 + x}\$ = \${100 × 20}/{100 + 20}\$ = \${50/3}\$, which is same as: \$16{2/3}\$%.

### Question 5

One number is 76 more than the other, and it is 69% of the sum of them. What is the number?

A

138.

B

238.

C

438.

D

338.

Soln.
Ans: a

Let the numbers be x and x - 76. We have been given x = \$69/100\$ × (x + x - 76), which gives 100x = 69 × (2x - 76), solving, we get x = 138. 