A water tank is initially 2/5 full. Pipe A can fill the entire tank in 10 minutes, while Pipe B can empty a full tank in 6 minutes. If both pipes are opened together from this initial state, how long will it take to reach an empty or full condition? State which occurs.

Introduction / Context:
The net rate determines whether the level rises or falls. Starting at 2/5 full, compute the combined rate of A (filling) and B (emptying). If the net is negative, the tank will empty; otherwise, it will fill. Then compute the time to reach the respective boundary (0 or 1 tank).

Given Data / Assumptions:

• A = +1/10 tank/min.
• B = −1/6 tank/min.
• Initial content = 2/5 of capacity.

Concept / Approach:
Net rate r = 1/10 − 1/6 = −1/15 tank/min ⇒ the tank drains. Time to empty = (current content) / (|r|).

Step-by-Step Solution:

Verification / Alternative check:
In 6 minutes at net −1/15, removed volume = 6/15 = 2/5, exactly the current content.

Why Other Options Are Wrong:
Options implying filling contradict the negative net rate.

Common Pitfalls:
Misinterpreting the sign of the net rate; always subtract the emptying pipe’s contribution.

Final Answer:
6 minutes to empty