# Alligations and Mixtures Quiz Set 012

### Question 1

A milkman has 24 liters of 12% curd, and 16 liters of 2% curd. If he mixes equal quantities of the two curd samples, then what is the percentage curd in the mixture?

A

8%.

B

9%.

C

7%.

D

11%.

Soln.
Ans: c

Quantities are equal, so answer = (12/100 + 2/100) X 100 = 7%.

### Question 2

An electronics shop sold 12 TV sets at a 23% profit, and 6 Coolers at 2% profit. What is the average percentage profit earned by the shop?

A

16%.

B

17%.

C

15%.

D

19%.

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 = 23, n1 = 12, n2 = 6, we have 12 × (A - 23) = 6 × (2 - A), from where we get A = 16%. The "property" in the alligation formula could be percentage, speed, weight, price, etc.,

### Question 3

A mixture of milk and water contains 14 parts of milk and 9 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

${5/28}$.

B

$1{2/9}$.

C

$2{1/30}$.

D

$2{29/30}$.

Soln.
Ans: a

Let the volume of the mixture be 14 + 9 = 23 liters. If x liters of the mixture is removed and replaced by water, the volume of water in the new mixture is $9 - {9x}/23 + x$. The volume of the milk in the new mixture would be $14 - {14x}/23.$ Equating the two volumes and solving for x we get x = ${23 × 5}/{2 × 14}$. The fraction that must be removed = $1/23$ × ${23 × 5}/{2 × 14}$, which gives $5/{2 × 14}$ = ${5/28}$.

### Question 4

In what ratio should water and wine be mixed so that after selling the mixture at cost price a profit of 25% is made?

A

${1/4}$.

B

$1{2/3}$.

C

$1{1/2}$.

D

$2{1/6}$.

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 25%, then 1 part of pure water is sold at the cost of 4 parts of wine. So the required mixing ratio should be 1 : 4.

### Question 5

The average weight of a class of 20 students is 3 Kg, and the average weight of a class of 40 students is 9 Kg. What is the average weight of the two combined classes?

A

7 Kg.

B

8 Kg.

C

6 Kg.

D

10 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 = 20, A1 = 3, n2 = 40 and A2 = 9, we get A = 7 Kg. 