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

The Correct Option is C

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)