A cistern has three pipes: Inlet A fills it in 2 hours, Inlet B fills it in 3 hours, and Pipe C is a waste (outlet). When all three are opened together, 7/24 of the cistern is filled in 30 minutes. How long does C alone take to empty a full cistern?

Introduction / Context:
The partial fill over a known time gives the net rate with all three pipes open. Subtract the two inlet rates to determine the (negative) waste rate and invert to get C’s emptying time.

Given Data / Assumptions:

• A = 1/2 tank/hour.
• B = 1/3 tank/hour.
• All three in 0.5 hour fill 7/24 ⇒ net rate = (7/24) / 0.5 = 7/12 tank/hour.

Concept / Approach:
Let c be C’s (negative) rate. Then 1/2 + 1/3 + c = 7/12 ⇒ solve for c and invert.

Step-by-Step Solution:

Verification / Alternative check:
Net = 5/6 − 1/4 = 10/12 − 3/12 = 7/12, consistent.

Why Other Options Are Wrong:
3/5/6 hours give different net rates and contradict the observed 7/24 in 30 minutes.

Common Pitfalls:
Forgetting to double the half-hour fill to get an hourly rate.

Final Answer:
4 hours