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### Question 1

In what ratio should a vendor mix two types of pulses costing Rs. 19/Kg and Rs. 4/Kg respectively so as to get a mixture of Rs. 14/Kg?

**A**

2.

**B**

3.

**C**

4.

**D**

$1{2/3}$.

**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} = 4, A_{1} = 19, A = 14 we have n_{1} × (14 - 19) = n_{2} × (4 - 14), from where we get the required ratio as $n_1/n_2 = 2 : 1$.

### Question 2

18 Kg of Grade I sugar costing Rs. 7/Kg is mixed with 9 Kg of Grade II sugar costing Rs. 16/Kg. What is the price of the mixture per Kg?

**A**

Rs. 10 per Kg.

**B**

Rs. 11 per Kg.

**C**

Rs. 9 per Kg.

**D**

Rs. 13 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} = 16, A_{1} = 7, n1 = 18, n2 = 9, we have 18 × (A - 7) = 9 × (16 - A), from where we get A = Rs. 10 per Kg.

### Question 3

Mr. X travels 8 km at a speed of 23 km/h, and 16 km at a speed of 17 km/h. What is the average speed during the entire journey?

**A**

19 km/h.

**B**

20 km/h.

**C**

18 km/h.

**D**

22 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} = 17, A_{1} = 23, n1 = 8, n2 = 16, we have 8 × (A - 23) = 16 × (17 - A), from where we get A = 19 km/h. *The "property" in the alligation formula could be speed, weight, price, etc.,*

### Question 4

A mixture of milk and water contains 47 parts of milk and 6 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**

${41/94}$.

**B**

$1{14/31}$.

**C**

$2{37/96}$.

**D**

$3{35/96}$.

**Soln.**

**Ans: a**

Let the volume of the mixture be 47 + 6 = 53 liters. If x liters of the mixture is removed and replaced by water, the volume of water in the new mixture is $6 - {6x}/53 + x$. The volume of the milk in the new mixture would be $47 - {47x}/53.$ Equating the two volumes and solving for x we get x = ${53 × 41}/{2 × 47}$. The fraction that must be removed = $1/53$ × ${53 × 41}/{2 × 47}$, which gives $41/{2 × 47}$ = ${41/94}$.

### Question 5

12 Kg of Grade I sugar costing Rs. 23/Kg is mixed with 4 Kg of Grade II sugar costing Rs. 11/Kg. What is the price of the mixture per Kg?

**A**

Rs. 20 per Kg.

**B**

Rs. 21 per Kg.

**C**

Rs. 19 per Kg.

**D**

Rs. 23 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} = 11, A_{1} = 23, n1 = 12, n2 = 4, we have 12 × (A - 23) = 4 × (11 - A), from where we get A = Rs. 20 per Kg.

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This Blog Post/Article "Alligations and Mixtures Quiz Set 006" 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