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### Question 1

Mr. X travels 12 km at a speed of 19 km/h, and 4 km at a speed of 3 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} = 3, A_{1} = 19, n1 = 12, n2 = 4, we have 12 × (A - 19) = 4 × (3 - A), from where we get A = 15 km/h. *The "property" in the alligation formula could be speed, weight, price, etc.,*

### Question 2

In what ratio should a vendor mix two types of pulses costing Rs. 10/Kg and Rs. 24/Kg respectively so as to get a mixture of Rs. 20/Kg?

**A**

${2/5}$.

**B**

$1{3/4}$.

**C**

$1{5/7}$.

**D**

$2{3/7}$.

**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} = 24, A_{1} = 10, A = 20 we have n_{1} × (20 - 10) = n_{2} × (24 - 20), from where we get the required ratio as $n_1/n_2 = 2 : 5$.

### Question 3

A mixture of milk and water contains 14 parts of milk and 5 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**

${9/28}$.

**B**

$1{10/27}$.

**C**

$2{1/6}$.

**D**

$3{1/10}$.

**Soln.**

**Ans: a**

Let the volume of the mixture be 14 + 5 = 19 liters. If x liters of the mixture is removed and replaced by water, the volume of water in the new mixture is $5 - {5x}/19 + x$. The volume of the milk in the new mixture would be $14 - {14x}/19.$ Equating the two volumes and solving for x we get x = ${19 × 9}/{2 × 14}$. The fraction that must be removed = $1/19$ × ${19 × 9}/{2 × 14}$, which gives $9/{2 × 14}$ = ${9/28}$.

### Question 4

In what ratio should water and wine be mixed so that after selling the mixture at cost price a profit of 10% is made?

**A**

${1/10}$.

**B**

$1{2/9}$.

**C**

$1{3/4}$.

**D**

$2{7/12}$.

**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 10%, then 1 part of pure water is sold at the cost of 10 parts of wine. So the required mixing ratio should be 1 : 10.

### Question 5

24 liters of Petrol costing Rs. 18/liter is mixed with 6 liters of Kerosene costing Rs. 3/liter. What is the price of the mixture per liter?

**A**

Rs. 15 per liter.

**B**

Rs. 16 per liter.

**C**

Rs. 14 per liter.

**D**

Rs. 18 per liter.

**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} = 3, A_{1} = 18, n1 = 24, n2 = 6, we have 24 × (A - 18) = 6 × (3 - A), from where we get A = Rs. 15 per liter.

This Blog Post/Article "Alligations and Mixtures Quiz Set 003" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Updated on 2019-08-18.