# Ratio and Proportion Quiz Set 010

### Question 1

What is the value of the first part if 160 is divided in the ratio \$3/2\$ : \$3/2\$ : \$7/3\$?

A

45.

B

49.

C

41.

D

53.

Soln.
Ans: a

We have \$3/2\$ : \$3/2\$ : \$7/3\$. Now 6 is the LCM of 2, 2 and 3, so the ratios become \$3/2 × 6\$ : \$3/2 × 6\$ : \$7/3 × 6\$, which are same as 9 : 9 : 14. The value of the first item is \$9/{9 + 9 + 14}\$ × 160 = 45.

### 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 350 liter mixture of milk and water contains 78% milk. How many more liters of water should be added so that the proportions of milk and water become equal?

A

196 liter.

B

197 liter.

C

195 liter.

D

199 liter.

Soln.
Ans: a

The volume of milk will remain same at \${78 × 350}/100\$ = 273 liters. The amount of water at present is 350 - 273 = 77 liters. We need to make the volume of water equal to that of the milk. So we have to add 273 - 77 = 196 liters of water.

### Question 4

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 5

If 50% of a number is equal to 2/7 of another number, then what is the ratio of first number to second number?

A

\${4/7}\$.

B

\$1{5/6}\$.

C

2.

D

\$2{7/9}\$.

Soln.
Ans: a

We have \${50A}/100 = {2B}/7\$, which can be re-arranged to \$A/{2 × 100} = B/{50 × 7}\$, so the required ratio is (2 × 100) : (50 × 7), which is 4 : 7. So the answer is \${4/7}\$. 