Question

The circumference of an inlet pipe and an outlet pipe is 15 cm and 10 cm respectively. How long will it take the tank to be filled, when it is empty and both pipes are opened?

Statement (1): Outlet pipe can empty the tank in 25 minutes.
Statement (2): Inlet pipe can fill the empty tank in 56 minutes.

• A. If the data in statement (1) alone is sufficient to answer the question, but the data in statement (2) alone is not sufficient.
• B. If the data in statement (2) alone is sufficient to answer the question, but the data in statement (1) alone is not sufficient.
• C. If the data in both the statements together are needed to answer the question.
• D. If either statement (1) alone or statement (2) alone is sufficient to answer the question.
• E. If the data in neither statement (1) nor statement (2) is sufficient to answer the question, and more data is needed.

Hint:

Ignore the pipe circumferences; you just need each pipe's individual fill/empty rate, and each statement gives only one of the two.

Answer 1

The Correct Option is C

The pipe circumferences (15 cm and 10 cm) given in the question are not actually usable on their own to find filling time without extra information relating pipe size to flow rate, so they are extra information here; what we really need is the individual filling and emptying rates of the two pipes.

Statement (1): Tells us the outlet pipe alone can empty the full tank in 25 minutes, i.e. outlet rate = \(1/25\) of the tank per minute. But we are given nothing about the inlet pipe's rate, so we cannot find the combined effect of both pipes running together. Not sufficient alone.

Statement (2): Tells us the inlet pipe alone fills the tank in 56 minutes, i.e. inlet rate = \(1/56\) of the tank per minute. But nothing is said about the outlet pipe's rate here, so again the combined effect cannot be found. Not sufficient alone.

Combining both statements: inlet rate = \(1/56\) per minute, outlet rate = \(1/25\) per minute (pipe emptying, so it works against filling). Net rate = \(1/56 - 1/25\), which is negative (outlet drains faster than inlet fills), so the tank would in fact never be filled, but this IS a definite, computable conclusion using both statements together.
So both statements together are required, and neither works alone. The correct choice is (c).