Question

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 $\frac{1}{2}$ 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. 20 litres
• B. 10 litres
• C. 40 litres
• D. 20$\frac{3}{4}$

Answer 1

Answer: (C)

40 litres

Answer 2

A can hold $\frac{1}{2}$ a litre of water, and B = $\frac{1}{4}$ litre of water can hold.
In the one complete operation, the water transferred will be = 1 - ($\frac{1}{2}$) = $\frac{1}{2}$ liters as 1 liter goes from Y to X. So 1 liter is contained in X.
But $\frac{1}{2}$ liter goes from X to Y as well. So net $\frac{1}{2}$ liters remain in X. If it takes 40 operations to equate water level,
= 40 × ($\frac{1}{2}$) = 20 liters is contained by both X and Y.
So the total volume of water in the system will be 40 litres
The correct option is (C)