Net filling with one inlet and one outlet A cistern can be filled by inlet A in 4 hours. An outlet B can empty the cistern in 8 hours. If both A and B are opened simultaneously, after how much time will the cistern become full?

Introduction / Context:Classic “pipes and cisterns” problems reduce to adding or subtracting constant rates. Inlets add volume; outlets remove volume. When they run together, the effective rate is the algebraic sum of their individual rates.

Given Data / Assumptions:

• Inlet A fills 1 tank in 4 h.
• Outlet B empties 1 tank in 8 h.
• Rates are constant; tank volume is normalized to 1 unit.

Concept / Approach:Rate(inlet) = 1/4 tank per hour. Rate(outlet) = 1/8 tank per hour (negative in net arithmetic). Net rate when both are open = 1/4 − 1/8.

Step-by-Step Solution:

Verification / Alternative check:In 8 h, A contributes 8*(1/4) = 2 tanks while B removes 8*(1/8) = 1 tank. Net = 1 tank filled.

Why Other Options Are Wrong:

• 6 h, 5 h, 7 h imply net rates of 1/6, 1/5, or 1/7, none equals 1/8.
• None of these is unnecessary because 8 h matches perfectly.

Common Pitfalls:Forgetting to subtract the outlet or averaging times instead of rates.

Final Answer:8 h