Question

A jar contains mixture of two liquids a & b in the ratio 4:1.when 10 litres of the liquid b is poured in tobthe jar the ratio becomes 2:3.how many litres of liquid a was contained in the jar?

Answer 1

Let the volume of the initial total mixture was V. When 10L of mixture is removed the volume becomes (V - 10). The concentration stays 4:1. 
Next step, when you add 10 litres of B, the amount of A does not change. 
So 
Amount of A in original mix = Amount of A in final mix
C1 * V1 = C2 * V2 
(4/5)*(V - 10) = (2/5)*V
1 - 10/V = 1/2
V = 20

So volume of A in initial mixture was (4/5) * 20 = 16 litres

Answer 2

Let the quantities of A and B in the original mixture be 4x and x litres.

According to the question, when 10 litres of the liquid B is poured into the jar

4x/(x+10) = 2/3

12x = 2x + 20

x = 2

The quantity in the original mixture = 4x +x=9 liters