# Alligations and Mixtures Quiz Set 010

### Question 1

A 400 liter mixture of milk and water contains 58% milk. How many more liters of water should be added so that the proportions of milk and water become equal?

A

64 liter.

B

65 liter.

C

63 liter.

D

67 liter.

Soln.
Ans: a

The volume of milk will remain same at ${58 × 400}/100$ = 232 liters. The amount of water at present is 400 - 232 = 168 liters. We need to make the volume of water equal to that of the milk. So we have to add 232 - 168 = 64 liters of water.

### Question 2

The average weight of a class of 30 students is 13 Kg, and the average weight of a class of 60 students is 7 Kg. What is the average weight of the two combined classes?

A

9 Kg.

B

10 Kg.

C

8 Kg.

D

12 Kg.

Soln.
Ans: a

If a sample n1 has a weighted average of A1, and another sample n2 has a weighted average of A2, then the weighted average, A,of the combined samples is determined by the alligation formula as: n1(A - A1) = n2(A2 - A). Putting n1 = 30, A1 = 13, n2 = 60 and A2 = 7, we get A = 9 Kg.

### Question 3

In what ratio should water and wine be mixed so that after selling the mixture at cost price a profit of 20% is made?

A

${1/5}$.

B

$1{1/2}$.

C

$1{4/7}$.

D

$2{2/7}$.

Soln.
Ans: a

The water will be sold at the price of wine. So the profit will be earned by selling water as wine. Profit% = $\text"Profit"/\text"Cost"$ × 100. If profit percent is 20%, then 1 part of pure water is sold at the cost of 5 parts of wine. So the required mixing ratio should be 1 : 5.

### Question 4

Two types of petrols having the prices per liter as Rs. 23 and Rs. 20 are mixed in the ratio 24 : 12. What is the price of the mixture per liter?

A

Rs. 22 per liter.

B

Rs. 23 per liter.

C

Rs. 21 per liter.

D

Rs. 25 per liter.

Soln.
Ans: a

If a sample n1 has an average price of A1, and another sample n2 has an average price of A2, then the price of the mixture, A, is determined by the alligation formula as: n1(A - A1) = n2(A2 - A). Putting A2 = 20, A1 = 23, n1 = 24, n2 = 12, we have 24 × (A - 23) = 12 × (20 - A), from where we get A = Rs. 22 per liter.

### Question 5

Mr. X travels 13 km at a speed of 19 km/h, and 4 km at a speed of 2 km/h. What is the average speed during the entire journey?

A

15 km/h.

B

16 km/h.

C

14 km/h.

D

18 km/h.

Soln.
Ans: a

We shall use the alligation formula. If a sample n1 has an average property of A1, and another sample n2 has an average property of A2, then the average property of the mixture, A, is determined by the alligation formula as: n1(A - A1) = n2(A2 - A). Putting A2 = 2, A1 = 19, n1 = 13, n2 = 4, we have 13 × (A - 19) = 4 × (2 - A), from where we get A = 15 km/h. The "property" in the alligation formula could be speed, weight, price, etc., 