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### Question 1

The average weight of a class of 80 students is 11 Kg, and the average weight of a class of 160 students is 11 Kg. What is the average weight of the two combined classes?

**A**

11 Kg.

**B**

12 Kg.

**C**

10 Kg.

**D**

14 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} = 11, n_{2} = 160 and A_{2} = 11, we get A = 11 Kg.

### Question 2

In what ratio should a vendor mix two types of pulses costing Rs. 16/Kg and Rs. 21/Kg respectively so as to get a mixture of Rs. 18/Kg?

**A**

$1{1/2}$.

**B**

$2{1/2}$.

**C**

$3{1/2}$.

**D**

$2{1/4}$.

**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} = 16, A = 18 we have n_{1} × (18 - 16) = n_{2} × (21 - 18), from where we get the required ratio as $n_1/n_2 = 3 : 2$.

### Question 3

A milkman has 4 liters of 23% curd, and 24 liters of 9% curd. If he mixes equal quantities of the two curd samples, then what is the percentage curd in the mixture?

### Question 4

The average weight of the students of a class is 4 Kg, and the average weight of the students of another class is 14 Kg. What is the ratio of the number of students in the two classes if the combined average weight is 13 Kg?

**A**

${1/9}$.

**B**

$1{1/4}$.

**C**

$1{8/11}$.

**D**

$2{6/11}$.

**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} = 14, A_{1} = 4, and A = 13, we have ${14 - 13}/{13 - 4 }$, from where we get the ratio as ${1/9}$.

### Question 5

12 liters of Petrol costing Rs. 5/liter is mixed with 6 liters of Kerosene costing Rs. 14/liter. What is the price of the mixture per liter?

**A**

Rs. 8 per liter.

**B**

Rs. 9 per liter.

**C**

Rs. 7 per liter.

**D**

Rs. 11 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} = 14, A_{1} = 5, n1 = 12, n2 = 6, we have 12 × (A - 5) = 6 × (14 - A), from where we get A = Rs. 8 per liter.

### More Chapters | See All...

Problems on Ages | Mirror Images | Profit and Loss | Partnerships | Basic Simplification | Course of Action | Distance and Time | Ranking Test | Averages | Data Sufficiency | More...

This Blog Post/Article "Alligations and Mixtures Quiz Set 007" 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