Two pipes A and B can fill a tank in 16 hours and 12 hours respectively. The capacity of the tank is 240 litres. If both pipes are opened together and then closed after 2 hours, how many more litres of water are still needed to fill the tank completely?

Introduction / Context:
This problem combines the idea of fractional tank filling with an actual volume in litres. Two pipes fill the tank together for a limited time, and we must determine the remaining volume needed to fill the tank completely. It is an application of rates, fractions of work done, and unit conversion to litres.

Given Data / Assumptions:
- Pipe A fills the entire tank in 16 hours
- Pipe B fills the entire tank in 12 hours
- Tank capacity = 240 litres
- Both pipes run together for 2 hours and then are closed
- No leakage or overflow is present

Concept / Approach:
We first compute the combined fraction of the tank filled in the 2 hours using their rates in terms of the fraction of the tank per hour. Then we convert this fraction to litres to get water already stored and subtract from the total capacity to find the remaining volume.

Step-by-Step Solution:
Step 1: Rate of pipe A = 1/16 tank per hour. Step 2: Rate of pipe B = 1/12 tank per hour. Step 3: Combined rate = 1/16 + 1/12 = (3 + 4) / 48 = 7/48 tank per hour. Step 4: In 2 hours they fill fraction = 2 * 7/48 = 14/48 = 7/24 of the tank. Step 5: Fraction of tank still empty = 1 - 7/24 = 17/24. Step 6: Remaining volume in litres = 17/24 * 240 = 17 * 10 = 170 litres.

Verification / Alternative check:
We can also compute the volume already filled: 7/24 of 240 = 7 * 10 = 70 litres. The tank capacity is 240 litres, so remaining = 240 - 70 = 170 litres. Both methods match, which confirms the calculation.

Why Other Options Are Wrong:
70 litres: This is the amount already filled, not the amount remaining.
90 litres: Corresponds to an incorrect fraction of the tank and does not match either method.
190 litres: Would imply that only 50 litres have been filled, which conflicts with the calculated combined rate of the two pipes.

Common Pitfalls:
Students often mix up the filled part with the remaining part. Another frequent error is to add the times directly instead of the rates. Also, some may forget to convert the fractional result of the tank into litres using the given total capacity, which is essential when the answer is expected in litres.

Final Answer:
After closing both pipes, an additional 170 litres of water are needed to fill the tank completely.