# Ratio and Proportion Quiz Set 006

### Question 1

A 250 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

140 liter.

B

141 liter.

C

139 liter.

D

143 liter.

Soln.
Ans: a

The volume of milk will remain same at \${78 × 250}/100\$ = 195 liters. The amount of water at present is 250 - 195 = 55 liters. We need to make the volume of water equal to that of the milk. So we have to add 195 - 55 = 140 liters of water.

### Question 2

What is the ratio A : B : C if A = \$6/5\$B and B = \$15/4\$C?

A

18 : 15 : 4.

B

6 : 15 : 4.

C

5 : 15 : 4.

D

6 : 4 : 90.

Soln.
Ans: a

We can write B = \$5/6\$A. Now we can use B as the pivot and write \$5/6\$A = B = \$15/4\$C. Divide all three with 5 × 15 to get \$A/{6 × 15}\$ = \$B/{5 × 15}\$ = \$C/{4 × 5}\$. So the required ratio is 90 : 75 : 20. The answer is 18 : 15 : 4.

### Question 3

The sides of a triangle are in the ratio 4 : 6 : 3, which is the longest side, if the perimeter is 260?

A

120.

B

122.

C

118.

D

124.

Soln.
Ans: a

Let the sides be 4x, 6x and 3x. We have 4x + 6x + 3x = 260, or 13x = 260, which gives x = 20, so the longest side is 6 × x = 6 × 20 = 120.

### Question 4

If X is 40% more than Z, and Y is 30% more than Z, what is the ratio of X to Y?

A

\$1{1/13}\$.

B

\$2{1/4}\$.

C

\$2{2/3}\$.

D

\$3{8/15}\$.

Soln.
Ans: a

Clearly, X = \$(100 + 40)/100\$ × Z, and Y = \$(100 + 30)/100\$ × Z, which gives X : Y as \$(100 + 40)/(100 + 30)\$ = \$140/130\$ = \${14/13}\$, which is same as: \$1{1/13}\$

### Question 5

What is the value of the first part if 142 is divided in the ratio \$7/2\$ : \$6/7\$ : \$5/7\$?

A

98.

B

102.

C

94.

D

106.

Soln.
Ans: a

We have \$7/2\$ : \$6/7\$ : \$5/7\$. Now 14 is the LCM of 2, 7 and 7, so the ratios become \$7/2 × 14\$ : \$6/7 × 14\$ : \$5/7 × 14\$, which are same as 49 : 12 : 10. The value of the first item is \$49/{49 + 12 + 10}\$ × 142 = 98. 