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### 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 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} = 30, A_{1} = 13, n_{2} = 60 and A_{2} = 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 n_{1} has an average price of A_{1}, and another sample n_{2} has an average price of A_{2}, then the price of the mixture, A, is determined by the alligation formula as: n_{1}(A - A_{1}) = n_{2}(A_{2} - A). Putting A_{2} = 20, A_{1} = 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 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} = 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.,*

### More Chapters | See All...

Compound Interest | Partnerships | Paper Folding | Decimal Numbers | Course of Action | Problems on Trains | Profit and Loss | Problems on Numbers | Cubes and Dice | Mirror Images | More...

This Blog Post/Article "Alligations and Mixtures Quiz Set 010" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2019-08-18.