Two inlet pipes A and B can fill a tank in 40 minutes and 60 minutes, respectively. An outlet pipe C empties the tank. With all three pipes open together, the tank fills in 30 minutes. How long would C alone take to empty a full tank?

Introduction / Context:
Pipe-and-cistern problems use additive rates: inlets add to the fill rate while outlets subtract from it. Knowing the net fill time with all pipes open, we can isolate the outlet’s rate and invert to get its emptying time.

Given Data / Assumptions:

• A fills in 40 min ⇒ rate = 1/40 tank/min.
• B fills in 60 min ⇒ rate = 1/60 tank/min.
• With A, B, C open together, fill time = 30 min ⇒ net rate = 1/30 tank/min.
• C is an outlet ⇒ its rate is subtractive.

Concept / Approach:
Let rC be C’s emptying rate (tank/min). Then 1/30 = 1/40 + 1/60 − rC. Solve for rC and invert to get time.

Step-by-Step Solution:

Verification / Alternative check:
Net with all three: 1/24 − 1/120 = (5 − 1)/120 = 4/120 = 1/30, matches the given net time.

Why Other Options Are Wrong:
1 h/3 h/4 h/90 min lead to net rates different from 1/30 when recombined with A and B.

Common Pitfalls:
Adding rather than subtracting the outlet, or mishandling fractions.

Final Answer:
2 h