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 A once and water is transferred to Y from X using B once. If A can hold 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?

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For problems involving repeated operations, determine the net volume change per operation and multiply by the number of operations.
Updated On: Mar 7, 2025
  • 10 litres
  • 20 litres
  • 40 litres
  • \( 20 \frac{1}{4} \) litres
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The Correct Option is C

Solution and Explanation

Each operation transfers: \[ A - B = 1 - \frac{1}{2} = \frac{1}{2} \text{ litre} \] Since 40 operations are performed: \[ \frac{1}{2} \times 40 = 20 \text{ litres} \] Since the two vessels are identical and initially, Y is full while X is empty, the total system water must be twice the transferred water: \[ 20 \times 2 = 40 \text{ litres} \] Thus, the correct answer is 40 litres.
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