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### Question 1

In what ratio should water and wine be mixed so that after selling the mixture at cost price a profit of 50% is made?

**A**

${1/2}$.

**B**

$1{1/2}$.

**C**

$2{1/2}$.

**D**

$1{3/4}$.

**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 50%, then 1 part of pure water is sold at the cost of 2 parts of wine. So the required mixing ratio should be 1 : 2.

### Question 2

Two types of petrols having the prices per liter as Rs. 17 and Rs. 23 are mixed in the ratio 14 : 7. What is the price of the mixture per liter?

**A**

Rs. 19 per liter.

**B**

Rs. 20 per liter.

**C**

Rs. 18 per liter.

**D**

Rs. 22 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} = 23, A_{1} = 17, n1 = 14, n2 = 7, we have 14 × (A - 17) = 7 × (23 - A), from where we get A = Rs. 19 per liter.

### Question 3

Two types of petrols having the prices per liter as Rs. 2 and Rs. 16 are mixed in the ratio 6 : 8. What is the price of the mixture per liter?

**A**

Rs. 10 per liter.

**B**

Rs. 11 per liter.

**C**

Rs. 9 per liter.

**D**

Rs. 13 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} = 16, A_{1} = 2, n1 = 6, n2 = 8, we have 6 × (A - 2) = 8 × (16 - A), from where we get A = Rs. 10 per liter.

### Question 4

The average weight of the students of a class is 2 Kg, and the average weight of the students of another class is 6 Kg. What is the ratio of the number of students in the two classes if the combined average weight is 3 Kg?

**A**

3.

**B**

4.

**C**

2.

**D**

2.

**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). So the ratio is ${A_2 - A}/{A - A_1 }$. Putting A_{2} = 6, A_{1} = 2, and A = 3, we have ${6 - 3}/{3 - 2 }$, from where we get the ratio as 3.

### Question 5

The average weight of a class of 80 students is 9 Kg, and the average weight of a class of 160 students is 6 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} = 80, A_{1} = 9, n_{2} = 160 and A_{2} = 6, we get A = 7 Kg.

### More Chapters | See All...

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This Blog Post/Article "Alligations and Mixtures Quiz Set 008" 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