Concept of “Alligation”-06

Question: A jar contains a mixture of two liquids A and B in the ratio 3: 1. When 16 litres of the mixture is taken out and 9 litres of liquid B is poured into the jar, the ratio becomes 3 : 4. How many litres of liquid A was contained in the jar? [Ans. (e) None of these (21 liters)]   

(a) 36 liters (b) 20 liters   (c) 27 liters (d) 25 liters (e) None of these

Solution:

Detailed Solution:

Concept: In the method of “Alligation”, rate of the two mixtures are taken and the rate the final mixture (mixture of two mixtures) should also be given. Then, the ratio of the quantity of two mixtures can be determined. Out of these four variables, any variable can be determined, if all other three variables are given.

In the given question, a jar contains two liquids A and B in the ratio of 3:1. 16 liters of the mixture is taken out and 9 liters of liquid B is poured into the jar. Finally, the ratio of A and B in the mixture becomes 3: 4.

The part of liquid A in the mixture is ¾ and the part of liquid A in the second mixture is 0:1 (as it is only liquid B); while the rate of liquid A in the final mixture is 3/7.

The ratio of two mixtures in the jar is [3/7 – 0]: [3/4 – 3/7] = [3/7]: [3×(1/4 – 1/7)] = 3/7 : [(3×3)/(4×7) = 1: ¾ = 4:3

3 ≡ 9 liters; So, 4 ≡? = 16 liters

But, initial quantity of mixture was (12+16) liters = 28 liters in which the ratio of A and B was 3:1

4 ≡ 28 liters

So, 3 ≡? = 21 liters Ans.