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### 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?

### 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 n_{1} has an average property of A_{1}, and another sample n_{2} has an average property of A_{2}, then the average property of the mixture, A, is determined by the alligation formula as: n_{1}(A - A_{1}) = n_{2}(A_{2} - A). Putting A_{2} = 2, A_{1} = 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 n_{1} has a weighted average of A_{1}, and another sample n_{2} has a weighted average of A_{2}, then the weighted average, A,of the combined samples is determined by the alligation formula as: n_{1}(A - A_{1}) = n_{2}(A_{2} - A). Putting n_{1} = 20, A_{1} = 3, n_{2} = 40 and A_{2} = 9, we get A = 7 Kg.

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This Blog Post/Article "Alligations and Mixtures Quiz Set 012" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2020-02-07. Published on: 2016-05-07