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

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

A mixture of milk and water contains 14 parts of milk and 1 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

\${13/28}\$.

B

\$1{14/27}\$.

C

\$2{3/10}\$.

D

\$3{7/30}\$.

Soln.
Ans: a

Let the volume of the mixture be 14 + 1 = 15 liters. If x liters of the mixture is removed and replaced by water, the volume of water in the new mixture is \$1 - {1x}/15 + x\$. The volume of the milk in the new mixture would be \$14 - {14x}/15.\$ Equating the two volumes and solving for x we get x = \${15 × 13}/{2 × 14}\$. The fraction that must be removed = \$1/15\$ × \${15 × 13}/{2 × 14}\$, which gives \$13/{2 × 14}\$ = \${13/28}\$.

Question 4

If a : b is 17 : 9, then what is (4a - 3b) : (7a - 8b)?

A

\${41/47}\$.

B

\$1{21/23}\$.

C

\$2{37/49}\$.

D

\$3{5/7}\$.

Soln.
Ans: a

Simply substitute the values to get (4a - 3b) : (7a - 8b) as (4 × 17 - 3 × 9) : (7 × 17 - 8 × 9) = \$41/47\$ = \${41/47}\$.

Question 5

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.