Pipe A and Pipe B can fill a tank at the rate of 12 litres per minute and 10…
2025
Pipe A and Pipe B can fill a tank at the rate of 12 litres per minute and 10 litres per minute respectively. There is also a leakage in the same tank. What is the capacity of the tank?
Statement I: If A and B are opened simultaneously, the tank is filled in 5 hours 45 minutes, and the leakage drains the tank at the rate of 6 litres per minute.
Statement II: Due to the leak, a filled tank drains out in 15 hours 20 minutes. If A and B are opened simultaneously, the tank is filled in 5 hours 45 minutes.
- A.
If the data in Statement I alone is sufficient to answer the question, while the data in Statement II alone is not sufficient to answer the question.
- B.
If the data in Statement II alone is sufficient to answer the question, while the data in Statement I alone is not sufficient to answer the question.
- C.
If the data either in Statement I alone or in Statement II alone is sufficient to answer the question.
- D.
If the data in both Statements I and II together are necessary to answer the question.
Show answer & explanation
Correct answer: C
Concept: A statement in a data-sufficiency question is sufficient whenever the facts it gives, by themselves, fix one unique numerical value for what is asked -- it need not be the fastest route, only a unique one. For a tank filled by pipes with a leak, the governing relation is: net filling rate = (sum of the pipes' rates) minus (the leak's draining rate), and capacity = net rate multiplied by the time to fill an empty tank. Each statement must be tested on its own, without borrowing anything from the other.
Applying Statement I alone:
Net filling rate with both pipes and the leak running together = 12 + 10 - 6 = 16 litres per minute.
Fill time = 5 hours 45 minutes = 345 minutes.
Capacity = 16 x 345 = 5520 litres -- one unique value, so Statement I alone is sufficient.
Applying Statement II alone:
Let the leak alone drain at x litres per minute.
With both pipes and the leak running together, net rate = (22 - x) litres per minute, filling the tank in 345 minutes, so capacity = (22 - x) x 345.
The leak alone empties a full tank in 15 hours 20 minutes = 920 minutes, so capacity = x x 920.
Equating the two expressions: (22 - x) x 345 = x x 920, which solves to x = 6 litres per minute.
Substituting back, capacity = 6 x 920 = 5520 litres -- again one unique value, so Statement II alone is also sufficient.
Cross-check: both statements, using entirely separate data, independently arrive at the same tank capacity of 5520 litres -- confirming that neither statement needed anything borrowed from the other.
Conclusion: since each statement, taken alone, is sufficient, the correct choice is the one stating that either statement I alone or statement II alone is sufficient.