Two filling taps P and Q have constant rates of 40 litres per minute and 60 litres per minute respectively, and together they can fill a tank in 8 minutes. If a waste tap can empty the completely filled tank in 32 minutes, what is the rate of the waste tap in litres per minute?

Introduction / Context:
This question involves two filling taps with known individual rates and a waste tap that empties the full tank in a given time. From the filling rates, we can deduce the capacity of the tank. Using the emptying time, we can then find the emptying rate in litres per minute for the waste tap.

Given Data / Assumptions:
- Tap P inflow rate = 40 litres per minute
- Tap Q inflow rate = 60 litres per minute
- Together P and Q fill the tank in 8 minutes
- Waste tap empties a completely full tank in 32 minutes
- All rates are constant, and there are no other leaks or taps

Concept / Approach:
First we find the tank capacity by using the combined inflow when P and Q work together. Then, knowing that the waste tap empties this capacity in 32 minutes, we divide capacity by time to get its emptying rate. This is a straightforward application of capacity = rate * time.

Step-by-Step Solution:
Step 1: Combined inflow rate of P and Q = 40 + 60 = 100 litres per minute. Step 2: Time to fill the tank with P and Q together = 8 minutes. Step 3: Capacity of tank = combined rate * time = 100 * 8 = 800 litres. Step 4: Waste tap empties the full tank in 32 minutes. Step 5: Emptying rate of waste tap = tank capacity / emptying time = 800 / 32 litres per minute. Step 6: 800 / 32 = 25 litres per minute.

Verification / Alternative check:
If the waste tap runs alone at 25 litres per minute, in 32 minutes it removes 32 * 25 = 800 litres, which exactly matches the capacity found from the filling taps. This consistency confirms the calculation.

Why Other Options Are Wrong:
34, 22 and 18 litres per minute: These rates, when multiplied by 32 minutes, do not match the 800 litre capacity implied by the filling information. Therefore they cannot satisfy both the filling and emptying conditions of the problem.

Common Pitfalls:
A typical mistake is misinterpreting the initial line and thinking the combined rate is 40 litres in 8 minutes or similar. Another error is computing the wrong capacity due to arithmetic mistakes in multiplication. Writing the formula capacity = rate * time explicitly helps avoid confusion.

Final Answer:
The waste tap empties water at a rate of 25 litres per minute.