A tap can fill a tank in 25 minutes while another tap can empty it in 50 minutes. If both taps are opened together from empty, will the tank be filled or emptied, and in how many minutes?

Introduction / Context:Determine the net rate when a filler and an emptier operate simultaneously. If the filler is faster, the tank fills; otherwise, it empties. The time equals the reciprocal of the net rate.

Given Data / Assumptions:

• Filler: 25 minutes ⇒ +1/25 tank/min.
• Emptier: 50 minutes ⇒ −1/50 tank/min.

Concept / Approach:Net rate = 1/25 − 1/50 = (2 − 1)/50 = 1/50 tank/min (positive ⇒ filling).

Step-by-Step Solution:Net rate = 1/25 − 1/50 = 1/50 tank/min.Time to fill = 1 ÷ (1/50) = 50 minutes.

Verification / Alternative check:Check contributions in 50 minutes: filler adds 50*(1/25) = 2 tanks; emptier removes 50*(1/50) = 1 tank; net = 1 tank.

Why Other Options Are Wrong:20 or 25 minutes incorrectly assume higher net rates or net emptying.

Common Pitfalls:Subtracting times instead of rates; sign confusion about the outlet.

Final Answer:Tank is filled up in 50 minutes