# Ratio and Proportion Quiz Set 003

### Question 1

A sum of Rs. 9000 is to be divided among three partners, P, Q and R, in the ratio 6 : 5 : 4. What is the difference between the shares of P and Q?

A

Rs. 600.

B

Rs. 602.

C

Rs. 598.

D

Rs. 604.

Soln.
Ans: a

The difference of shares of Q is in the ratio like this: \${6 - 5}/{6 + 5 + 4} × 9000\$ = Rs. 600.

### Question 2

What is the ratio A : B : C if A = \$8/5\$B and B = \$19/2\$C?

A

152 : 95 : 10.

B

8 : 19 : 2.

C

5 : 19 : 2.

D

8 : 2 : 152.

Soln.
Ans: a

We can write B = \$5/8\$A. Now we can use B as the pivot and write \$5/8\$A = B = \$19/2\$C. Divide all three with 5 × 19 to get \$A/{8 × 19}\$ = \$B/{5 × 19}\$ = \$C/{2 × 5}\$. So the required ratio is 152 : 95 : 10. The answer is 152 : 95 : 10.

### Question 3

The ratio of shares of three friends in Rs. 2400 are in an A.P.(arithmtic progression). What is the share of the friend who is neither the richest, nor the poorest?

A

Rs. 800.

B

Rs. 804.

C

Rs. 796.

D

Rs. 808.

Soln.
Ans: a

Let the shares be in the ratio a - d : a : a + d. The value of the middle item is \$a/{(a - d) + a + (a + d)}\$ × 2400 = \$a/{3a}\$ × 2400 = \$2400/3\$ = Rs. 800.

### Question 4

A mixture of milk and water contains 2 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

\${1/4}\$.

B

\$1{2/3}\$.

C

\$1{1/2}\$.

D

\$2{1/6}\$.

Soln.
Ans: a

Let the volume of the mixture be 2 + 1 = 3 liters. If x liters of the mixture is removed and replaced by water, the volume of water in the new mixture is \$1 - {1x}/3 + x\$. The volume of the milk in the new mixture would be \$2 - {2x}/3.\$ Equating the two volumes and solving for x we get x = \${3 × 1}/{2 × 2}\$. The fraction that must be removed = \$1/3\$ × \${3 × 1}/{2 × 2}\$, which gives \$1/{2 × 2}\$ = \${1/4}\$.

### Question 5

What is the value of the first part if 2023 is divided in the ratio \$9/5\$ : \$2/3\$ : \$2/7\$?

A

1323.

B

1327.

C

1319.

D

1331.

Soln.
Ans: a

We have \$9/5\$ : \$2/3\$ : \$2/7\$. Now 105 is the LCM of 5, 3 and 7, so the ratios become \$9/5 × 105\$ : \$2/3 × 105\$ : \$2/7 × 105\$, which are same as 189 : 70 : 30. The value of the first item is \$189/{189 + 70 + 30}\$ × 2023 = 1323. 