# Alligations and Mixtures Quiz Set 008

### 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 n1 has an average price of A1, and another sample n2 has an average price of A2, then the price of the mixture, A, is determined by the alligation formula as: n1(A - A1) = n2(A2 - A). Putting A2 = 23, A1 = 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 n1 has an average price of A1, and another sample n2 has an average price of A2, then the price of the mixture, A, is determined by the alligation formula as: n1(A - A1) = n2(A2 - A). Putting A2 = 16, A1 = 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 n1 has a weighted average of A1, and another sample n2 has a weighted average of A2, then the weighted average, A,of the combined samples is determined by the alligation formula as: n1(A - A1) = n2(A2 - A). So the ratio is ${A_2 - A}/{A - A_1 }$. Putting A2 = 6, A1 = 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 n1 has a weighted average of A1, and another sample n2 has a weighted average of A2, then the weighted average, A,of the combined samples is determined by the alligation formula as: n1(A - A1) = n2(A2 - A). Putting n1 = 80, A1 = 9, n2 = 160 and A2 = 6, we get A = 7 Kg. 