A cistern has a leak that would empty it in 15 hours. A tap is turned on that admits water at 2 litres per hour into the cistern. With the leak and the inlet both open, the cistern now empties in 30 hours. What is the capacity of the cistern (in litres)?

Introduction / Context:The original stem with “10 hours” is contradictory (an inlet that admits water cannot shorten the emptying time). Applying the Recovery-First policy, we minimally repair the duration to “30 hours,” a standard solvable version that preserves the capacity-computation intent and aligns with typical textbook formulations.

Given Data / Assumptions (after minimal repair):

• Leak alone empties in 15 h ⇒ leak rate = V/15 litres/hour.
• Inlet admits +2 L/hour.
• With both, the tank empties in 30 h ⇒ net outflow = V/30 L/hour.

Concept / Approach:Net outflow = leak − inlet ⇒ V/15 − 2 = V/30. Solve for V, the capacity.

Step-by-Step Solution:

Verification / Alternative check:Leak = 60/15 = 4 L/h; net outflow with inlet = 4 − 2 = 2 L/h; at 2 L/h, emptying a full 60 L takes 30 h, consistent.

Why Other Options Are Wrong:50/45/360 litres do not satisfy V/15 − 2 = V/30.

Common Pitfalls:Noticing the original inconsistency: with a positive inlet, emptying time must increase, not decrease.

Final Answer:60 litres