There are two identical vessels X and Y. Y is filled with water to the brim and X is empty. There are two pails A and B, such that B can hold half as much water as A. One operation is said to be executed when water is transferred from Y to X using B once. If A can hold 1/2 a litre of water and it takes 40 operations to equate the water level in X and Y, what is the total volume of water in the system ?

A can hold 1/2 a litre of water, so B = 1/4 lt of water can hold.

In one complete operation, water transferred = 1 - (1/2) = 1/2 liters as 1 liter goes from Y to X. So 1 liter is contained in X. 

But 1/2 liter goes from X to Y as well. So net 1/2 liters remain in X. If it takes 40 operations to equate water level,
∴ 40 × (1/2) = 20 liters is contained in X and Y.

Hence total volume of water in the system is 40 litres