Final answer:
The cistern holds 60 liters, given the provided rates of emptying and filling, which contradicts the given multiple-choice options. We established the capacity by solving the equation derived from the combined rates of the leak and the tap.
Step-by-step explanation:
The question is a classic problem of combining rates of work to determine the capacity of the cistern. The leak empties the cistern at a rate that would take 10 hours to empty it completely. When a tap is added that contributes 2 liters per hour, the cistern now takes 15 hours to empty. This information allows us to set up an equation to solve for the cistern's capacity.
First, let's consider the rate at which the cistern is being emptied due to the leak. If the cistern is emptied in 10 hours, then in one hour, it leaks out 1/10 of its capacity. Now, when the tap is turned on, the cistern is emptied in 15 hours. This means that in one hour, the cistern loses 1/15 of its capacity. However, this is offset by the tap which adds 2 liters every hour.
The effective emptying rate when the tap is on is the leak rate minus the tap's fill rate. Combining the rates, we have (1/10 of the cistern's capacity) - 2 liters = (1/15 of the cistern's capacity). We want to find the capacity 'C' of the cistern. The equation is: 1/10 × C - 2 = 1/15 × C
To solve for C, we first get a common denominator for the fractions:
(3/30) × C - 2 = (2/30) × C
Now we can subtract (2/30)C from both sides:
(1/30) × C = 2
Multiplying both sides by 30 we get C = 60 liters. However, we assumed that we understand the leak and tap rates correctly, and there may have been an error in the problem statement, as none of the provided answer options match our result. Assuming the problem statement is correct and complete, the cistern holds 60 liters, but this is not one of the given options.