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### Question 1

9 Kg of Grade I sugar costing Rs. 6/Kg is mixed with 12 Kg of Grade II sugar costing Rs. 20/Kg. What is the price of the mixture per Kg?

**A**

Rs. 14 per Kg.

**B**

Rs. 15 per Kg.

**C**

Rs. 13 per Kg.

**D**

Rs. 17 per Kg.

**Soln.**

**Ans: a**

We shall use the alligation formula. 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} = 6, n1 = 9, n2 = 12, we have 9 × (A - 6) = 12 × (20 - A), from where we get A = Rs. 14 per Kg.

### Question 2

Mr. X travels 6 km at a speed of 18 km/h, and 3 km at a speed of 15 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 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} = 15, A_{1} = 18, n1 = 6, n2 = 3, we have 6 × (A - 18) = 3 × (15 - A), from where we get A = 17 km/h. *The "property" in the alligation formula could be speed, weight, price, etc.,*

### Question 3

3 Kg of Grade I sugar costing Rs. 13/Kg is mixed with 9 Kg of Grade II sugar costing Rs. 21/Kg. What is the price of the mixture per Kg?

**A**

Rs. 19 per Kg.

**B**

Rs. 20 per Kg.

**C**

Rs. 18 per Kg.

**D**

Rs. 22 per Kg.

**Soln.**

**Ans: a**

We shall use the alligation formula. 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} = 21, A_{1} = 13, n1 = 3, n2 = 9, we have 3 × (A - 13) = 9 × (21 - A), from where we get A = Rs. 19 per Kg.

### Question 4

A 150 liter mixture of milk and water contains 82% milk. How many more liters of water should be added so that the proportions of milk and water become equal?

**A**

96 liter.

**B**

97 liter.

**C**

95 liter.

**D**

99 liter.

**Soln.**

**Ans: a**

The volume of milk will remain same at ${82 × 150}/100$ = 123 liters. The amount of water at present is 150 - 123 = 27 liters. We need to make the volume of water equal to that of the milk. So we have to add 123 - 27 = 96 liters of water.

### Question 5

An electronics shop sold 16 TV sets at a 20% profit, and 4 Coolers at 5% profit. What is the average percentage profit earned by the shop?

**A**

17%.

**B**

18%.

**C**

16%.

**D**

20%.

**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} = 5, A_{1} = 20, n1 = 16, n2 = 4, we have 16 × (A - 20) = 4 × (5 - A), from where we get A = 17%. *The "property" in the alligation formula could be percentage, speed, weight, price, etc.,*

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This Blog Post/Article "Alligations and Mixtures Quiz Set 009" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2019-08-18.