# Ratio and Proportion Quiz Set 016

### Question 1

If a : b is 8 : 5, then what is (8a - 5b) : (9a - 6b)?

A

\${13/14}\$.

B

\$2{1/13}\$.

C

\$2{9/16}\$.

D

\$3{7/16}\$.

Soln.
Ans: a

Simply substitute the values to get (8a - 5b) : (9a - 6b) as (8 × 8 - 5 × 5) : (9 × 8 - 6 × 5) = \$39/42\$ = \${13/14}\$.

### Question 2

If 40% of a number is equal to 4/7 of another number, then what is the ratio of first number to second number?

A

\$1{3/7}\$.

B

\$2{5/6}\$.

C

\${1/3}\$.

D

\$3{4/9}\$.

Soln.
Ans: a

We have \${40A}/100 = {4B}/7\$, which can be re-arranged to \$A/{4 × 100} = B/{40 × 7}\$, so the required ratio is (4 × 100) : (40 × 7), which is 10 : 7. So the answer is \${10/7}\$, which is same as: \$1{3/7}\$.

### Question 3

Two numbers M and N are in ratio 17 : 2. If they are, respectively, increased by 30% and 70%, what will be the new ratio of M : N?

A

\$6{1/2}\$.

B

\$7{1/2}\$.

C

\$5{1/2}\$.

D

\$4{3/4}\$.

Soln.
Ans: a

New M will scale to \$130/100\$ × 17, and N to \$170/100\$ × 2. New ratio is \${130 × 17}/{170 × 2}\$ = \${13/2}\$, which is same as: \$6{1/2}\$.

### Question 4

The ratio of shares of three friends in Rs. 1200 are in an A.P.(arithmtic progression). What is the share of the friend who is neither the richest, nor the poorest?

A

Rs. 400.

B

Rs. 404.

C

Rs. 396.

D

Rs. 408.

Soln.
Ans: a

Let the shares be in the ratio a - d : a : a + d. The value of the middle item is \$a/{(a - d) + a + (a + d)}\$ × 1200 = \$a/{3a}\$ × 1200 = \$1200/3\$ = Rs. 400.

### Question 5

Two numbers are in the ratio 3 : 2. If both are decreased by 5, the new ratio becomes 52 : 33. What is the first number?

A

57.

B

61.

C

53.

D

65.

Soln.
Ans: a

Let the numbers be 3x and 2x. We are given \${3x - 5}/{2x - 5} = 52/33\$. Solving, we get x = 19, so first number is 19 × 3 = 57.