# Ratio and Proportion Quiz Set 016

### Question 1

Two numbers A and B are in ratio 8 : 9. If they are both increased by 40%, what will be the new ratio of A : B?

A

\${8/9}\$.

B

\$2{1/8}\$.

C

\$2{4/11}\$.

D

\$3{2/11}\$.

Soln.
Ans: a

New A will scale to \$140/100\$ × 8, and B to \$140/100\$ × 9. New ratio is \${140 × 8}/{140 × 9}\$ = \${8/9}\$.

### Question 2

A mixture of milk and water contains 43 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

\${17/43}\$.

B

\$1{3/7}\$.

C

\$2{13/45}\$.

D

\$3{11/45}\$.

Soln.
Ans: a

Let the volume of the mixture be 43 + 9 = 52 liters. If x liters of the mixture is removed and replaced by water, the volume of water in the new mixture is \$9 - {9x}/52 + x\$. The volume of the milk in the new mixture would be \$43 - {43x}/52.\$ Equating the two volumes and solving for x we get x = \${52 × 34}/{2 × 43}\$. The fraction that must be removed = \$1/52\$ × \${52 × 34}/{2 × 43}\$, which gives \$34/{2 × 43}\$ = \${17/43}\$.

### Question 3

If \$26/45\$ of A's amount is \$13/15\$ of B's amount, and the total amount they have is Rs. 1000, what is the amount with A?

A

Rs. 600.

B

Rs. 602.

C

Rs. 598.

D

Rs. 604.

Soln.
Ans: a

Let the amounts with them be A and B. So \$26/45\$A = \$13/15\$B, which can be re-arranged to get A : B = 3 : 2. So A = \$3/5 × 1000\$ = Rs. 600.

### Question 4

The sides of a triangle are in the ratio 2 : 14 : 13, which is the longest side, if the perimeter is 580?

A

280.

B

282.

C

278.

D

284.

Soln.
Ans: a

Let the sides be 2x, 14x and 13x. We have 2x + 14x + 13x = 580, or 29x = 580, which gives x = 20, so the longest side is 14 × x = 14 × 20 = 280.

### Question 5

If 10% of a number is equal to 4/13 of another number, then what is the ratio of first number to second number?

A

\$3{1/13}\$.

B

\$4{5/12}\$.

C

\$1{4/5}\$.

D

\$5{4/15}\$.

Soln.
Ans: a

We have \${10A}/100 = {4B}/13\$, which can be re-arranged to \$A/{4 × 100} = B/{10 × 13}\$, so the required ratio is (4 × 100) : (10 × 13), which is 40 : 13. So the answer is \${40/13}\$, which is same as: \$3{1/13}\$.