Question

Water is pumped into the completely empty tank at a constant rate through an inlet pipe. At the same time, there is a leak at the bottom of the tank which leaks water at a constant rate. How long it will take the tank get filled completely? (1) Total capacity of water the tank can hold is 120 gallons. (2) Inlet pipe can completely fill the empty tank in 10 hours if there is no leak in the tank, and also the leak at the bottom of the tank can completely empty the filled tank in 15 hours if there is no water pumped into the tank.

• A. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
• B. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
• C. Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
• D. Each statement alone is sufficient to answer the question.
• E. Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.

Hint:

When solving for time and rates, use the relationship between work done, rate, and time, and combine the given information to form a solvable system of equations.

Answer 1

The Correct Option is C

Step 1: Analyzing Statement 1.
Statement 1 tells us that the total capacity of the tank is 120 gallons, but it does not provide the rate of the pump or the leak, making it insufficient to solve the problem.
Step 2: Analyzing Statement 2.
Statement 2 gives us the time taken by the inlet pipe and the leak separately, but we still need the leak and pump rates to calculate the total time. Therefore, statement 2 alone is insufficient.
Step 3: Combining the statements.
When combining both statements, we now know that the tank's total capacity is 120 gallons, the rate of the inlet pipe, and the rate of the leak. By solving the system of equations, we can calculate the time required to fill the tank. Hence, both statements are together sufficient to answer the question.
Step 4: Conclusion.
The correct answer is (C).