A pipe can fill a tank in 20 hours. Due to a leak at the bottom, the tank actually gets filled in 40 hours. If the tank is full, how long will the leak alone take to empty it?

Introduction / Context:
A leak reduces the net filling rate. Comparing the normal fill rate with the slowed net rate lets us compute the leak’s own emptying rate and its corresponding emptying time.

Given Data / Assumptions:

• Inlet alone: 20 hours to fill ⇒ rate = 1/20 tank/hour.
• With leak present: 40 hours to fill ⇒ net rate = 1/40 tank/hour.
• Rates are constant throughout.

Concept / Approach:
leak rate = inlet rate − net rate. Emptying time of the leak is the reciprocal of this leak rate.

Step-by-Step Solution:
Inlet rate = 1/20.Net rate = 1/40.Leak rate = 1/20 − 1/40 = 1/40 tank/hour.Time to empty full tank = 1 / (1/40) = 40 hours.

Verification / Alternative check:
Check net: 1/20 − 1/40 = 1/40 ⇒ net fill time 40 hours, consistent.

Why Other Options Are Wrong:
30 h and 50 h reflect incorrect subtraction or inversion of rates.

Common Pitfalls:
Subtracting times (20 − 40) instead of rates; forgetting to invert to get time.

Final Answer:
40 h