A leak at the bottom of a tank can empty a full tank in 6 hours. An inlet supplies water at 4 litres per minute. When the tank is full, the inlet is opened; due to the leak, the tank becomes empty in 8 hours. What is the capacity of the tank (in litres)?

Introduction / Context:The leak removes water at a rate proportional to capacity, while the inlet adds a fixed 4 L/min. With both acting, the tank empties in 8 hours, which reveals the net outflow. Set up a rate equation in litres/hour for capacity V and solve for V.

Given Data / Assumptions:

• Leak alone: V/6 litres/hour outward.
• Inlet: +4 L/min = +240 L/hour.
• Net emptying time with both: 8 h ⇒ net outflow = V/8 L/hour.

Concept / Approach:V/6 − 240 = V/8. Solve for V to get capacity in litres.

Step-by-Step Solution:

Verification / Alternative check:Leak = 5760/6 = 960 L/h; inlet = 240 L/h; net outflow = 720 L/h; in 8 h, 8 * 720 = 5760 L, matching capacity.

Why Other Options Are Wrong:5260/5846/6970 do not satisfy the linear relation V/6 − 240 = V/8.

Common Pitfalls:Forgetting to convert 4 L/min to 240 L/h or reversing the leak and inlet signs.

Final Answer:5760 litres