# Alligations and Mixtures Quiz Set 003

### Question 1

Mr. X travels 12 km at a speed of 19 km/h, and 4 km at a speed of 3 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 = 3, A1 = 19, n1 = 12, n2 = 4, we have 12 × (A - 19) = 4 × (3 - A), from where we get A = 15 km/h. The "property" in the alligation formula could be speed, weight, price, etc.,

### Question 2

In what ratio should a vendor mix two types of pulses costing Rs. 10/Kg and Rs. 24/Kg respectively so as to get a mixture of Rs. 20/Kg?

A

${2/5}$.

B

$1{3/4}$.

C

$1{5/7}$.

D

$2{3/7}$.

Soln.
Ans: a

We shall use the alligation formula. 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 = 24, A1 = 10, A = 20 we have n1 × (20 - 10) = n2 × (24 - 20), from where we get the required ratio as $n_1/n_2 = 2 : 5$.

### Question 3

A mixture of milk and water contains 14 parts of milk and 5 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

${9/28}$.

B

$1{10/27}$.

C

$2{1/6}$.

D

$3{1/10}$.

Soln.
Ans: a

Let the volume of the mixture be 14 + 5 = 19 liters. If x liters of the mixture is removed and replaced by water, the volume of water in the new mixture is $5 - {5x}/19 + x$. The volume of the milk in the new mixture would be $14 - {14x}/19.$ Equating the two volumes and solving for x we get x = ${19 × 9}/{2 × 14}$. The fraction that must be removed = $1/19$ × ${19 × 9}/{2 × 14}$, which gives $9/{2 × 14}$ = ${9/28}$.

### Question 4

In what ratio should water and wine be mixed so that after selling the mixture at cost price a profit of 10% is made?

A

${1/10}$.

B

$1{2/9}$.

C

$1{3/4}$.

D

$2{7/12}$.

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 10%, then 1 part of pure water is sold at the cost of 10 parts of wine. So the required mixing ratio should be 1 : 10.

### Question 5

24 liters of Petrol costing Rs. 18/liter is mixed with 6 liters of Kerosene costing Rs. 3/liter. What is the price of the mixture per liter?

A

Rs. 15 per liter.

B

Rs. 16 per liter.

C

Rs. 14 per liter.

D

Rs. 18 per liter.

Soln.
Ans: a

We shall use the alligation formula. 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 = 3, A1 = 18, n1 = 24, n2 = 6, we have 24 × (A - 18) = 6 × (3 - A), from where we get A = Rs. 15 per liter. 