# Alligations and Mixtures Quiz Set 001

### Question 1

A mixture of milk and water contains 29 parts of milk and 14 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

${15/58}$.

B

$1{16/57}$.

C

$2{11/60}$.

D

$3{3/20}$.

Soln.
Ans: a

Let the volume of the mixture be 29 + 14 = 43 liters. If x liters of the mixture is removed and replaced by water, the volume of water in the new mixture is $14 - {14x}/43 + x$. The volume of the milk in the new mixture would be $29 - {29x}/43.$ Equating the two volumes and solving for x we get x = ${43 × 15}/{2 × 29}$. The fraction that must be removed = $1/43$ × ${43 × 15}/{2 × 29}$, which gives $15/{2 × 29}$ = ${15/58}$.

### Question 2

A 300 liter mixture of milk and water contains 70% milk. How many more liters of water should be added so that the proportions of milk and water become equal?

A

120 liter.

B

121 liter.

C

119 liter.

D

123 liter.

Soln.
Ans: a

The volume of milk will remain same at ${70 × 300}/100$ = 210 liters. The amount of water at present is 300 - 210 = 90 liters. We need to make the volume of water equal to that of the milk. So we have to add 210 - 90 = 120 liters of water.

### Question 3

In what ratio should water and wine be mixed so that after selling the mixture at cost price a profit of 5% is made?

A

${1/20}$.

B

$1{2/19}$.

C

$1{19/22}$.

D

$2{17/22}$.

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 5%, then 1 part of pure water is sold at the cost of 20 parts of wine. So the required mixing ratio should be 1 : 20.

### Question 4

Mr. X travels 6 km at a speed of 12 km/h, and 15 km at a speed of 19 km/h. What is the average speed during the entire journey?

A

17 km/h.

B

18 km/h.

C

16 km/h.

D

20 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 = 19, A1 = 12, n1 = 6, n2 = 15, we have 6 × (A - 12) = 15 × (19 - A), from where we get A = 17 km/h. The "property" in the alligation formula could be speed, weight, price, etc.,

### Question 5

9 liters of Petrol costing Rs. 21/liter is mixed with 15 liters of Kerosene costing Rs. 13/liter. What is the price of the mixture per liter?

A

Rs. 16 per liter.

B

Rs. 17 per liter.

C

Rs. 15 per liter.

D

Rs. 19 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 = 13, A1 = 21, n1 = 9, n2 = 15, we have 9 × (A - 21) = 15 × (13 - A), from where we get A = Rs. 16 per liter.