# Ratio and Proportion Quiz Set 020

### Question 1

If X is 70% more than Z, and Y is 50% more than Z, what is the ratio of X to Y?

A

\$1{2/15}\$.

B

\$2{2/7}\$.

C

\${2/17}\$.

D

\$3{11/17}\$.

Soln.
Ans: a

Clearly, X = \$(100 + 70)/100\$ × Z, and Y = \$(100 + 50)/100\$ × Z, which gives X : Y as \$(100 + 70)/(100 + 50)\$ = \$170/150\$ = \${17/15}\$, which is same as: \$1{2/15}\$

### Question 2

Two numbers M and N are in ratio 13 : 9. If they are, respectively, increased by 60% and 30%, what will be the new ratio of M : N?

A

\$1{7/9}\$.

B

\$3{1/8}\$.

C

\${7/11}\$.

D

\$3{10/11}\$.

Soln.
Ans: a

New M will scale to \$160/100\$ × 13, and N to \$130/100\$ × 9. New ratio is \${160 × 13}/{130 × 9}\$ = \${16/9}\$, which is same as: \$1{7/9}\$.

### Question 3

A mixture of milk and water contains 11 parts of milk and 9 parts of water. How much fraction of the mixture should be removed and replaced by water so that ratio of water and milk becomes equal?

A

\${1/11}\$.

B

\$1{1/5}\$.

C

\$1{10/13}\$.

D

\$2{8/13}\$.

Soln.
Ans: a

Let the volume of the mixture be 11 + 9 = 20 liters. If x liters of the mixture is removed and replaced by water, the volume of water in the new mixture is \$9 - {9x}/20 + x\$. The volume of the milk in the new mixture would be \$11 - {11x}/20.\$ Equating the two volumes and solving for x we get x = \${20 × 2}/{2 × 11}\$. The fraction that must be removed = \$1/20\$ × \${20 × 2}/{2 × 11}\$, which gives \$2/{2 × 11}\$ = \${1/11}\$.

### Question 4

What is the ratio A : B : C if A = \$7/9\$B and B = \$18/17\$C?

A

14 : 18 : 17.

B

7 : 18 : 17.

C

9 : 18 : 17.

D

7 : 17 : 126.

Soln.
Ans: a

We can write B = \$9/7\$A. Now we can use B as the pivot and write \$9/7\$A = B = \$18/17\$C. Divide all three with 9 × 18 to get \$A/{7 × 18}\$ = \$B/{9 × 18}\$ = \$C/{17 × 9}\$. So the required ratio is 126 : 162 : 153. The answer is 14 : 18 : 17.

### Question 5

A sum of Rs. 16100 is to be divided among three partners, P, Q and R, in the ratio 11 : 9 : 3. What is the difference between the shares of P and Q?

A

Rs. 1400.

B

Rs. 1402.

C

Rs. 1398.

D

Rs. 1404.

Soln.
Ans: a

The difference of shares of Q is in the ratio like this: \${11 - 9}/{11 + 9 + 3} × 16100\$ = Rs. 1400.