Question:medium

A pipe can fill a tank in 6 hours, while a leak not at the bottom of the tank can empty upto it in 3 hours. If both are operated simultaneously and initially the tank is full, when the tank will be full upto the height of the leak?
Statement 1: The leak is developed at a one-third height of the tank
Statement 2: The leak takes 3 hours to empty the tank upto its height

Updated On: Jan 13, 2026
  • Statement (1) alone is sufficient to answer the question
  • Statement (2) alone is sufficient to answer the question
  • Both the statements together are needed to answer the question
  • Either statement (1) alone or statement (2) alone is sufficient to answer the question
  • Neither statement (1) nor statement (2) suffices to answer the question
Show Solution

The Correct Option is A

Solution and Explanation

The correct answer is option (A):
Statement (1) alone is sufficient to answer the question

The question asks when a tank, initially full, will be filled up to the height of a leak. We're given information about filling and emptying rates. Let's analyze the statements:

Statement 1: The leak is developed at a one-third height of the tank.

If the leak is at one-third height, and the tank is initially full, we only need to know how the water level changes *above* the leak. The pipe fills the tank completely in 6 hours. Let's say the total capacity of the tank is 6 units (a convenient choice since we're given the fill time is 6 hours). This means the pipe fills 1 unit per hour. The leak empties the *entire* tank in 3 hours. Since the leak is at one-third height, let's suppose that the tank is 6 units high so that the leak is at 2 units (6 * 1/3) height.

Initially, the tank is full, so the water level is at 6 units. The leak is at 2 units. The water has to fall to the height of the leak, so a quantity of 4 units (6-2) needs to be removed. The net rate of water decrease above the leak when both pipe and leak are open is not important. If the water level is above the leak, the water is going to go through the leak. The leak empties the tank at 2 units height at a specific time and that’s what we are looking for. We don’t need the information of how long the leak would be at one-third height and if the pipe is open. So with the information that the leak is at one third height of the tank we can determine when the water has dropped to that level. Since the tank is initially full, we can calculate how long it takes to drop to 1/3 height. The rate of the leak is 2 unit/hour which means it will take 1 hour to reach to the 1/3 height.

Statement 2: The leak takes 3 hours to empty the tank up to its height.

This statement gives us information about how the leak behaves, but without knowing the *height* of the leak, we can't determine *when* the water reaches that height. We need the leak's position to solve the problem.

Therefore, statement 1 alone is sufficient. The height of the leak is what matters most.
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