A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. If pipe B is used alone for the first half of the total time and then both pipes A and B are used together for the second half, how many minutes in total are required to fill the tanker completely from empty?

Introduction / Context:
This question checks understanding of variable rates over different time intervals. A slower and a faster pipe are operated in different combinations during two equal halves of the total filling time. We must correctly express the filled fraction in each half and ensure that the sum equals one full tank.

Given Data / Assumptions:
- Pipe A alone fills the tank in 60 minutes
- Pipe B alone fills the tank in 40 minutes
- For the first half of the total time only pipe B is used
- For the second half of the total time both A and B are used together
- Tank is initially empty and there is no leakage

Concept / Approach:
Let the total filling time be t minutes. Then each half period lasts t/2 minutes. In the first half we use only the rate of B, and in the second half we use the combined rates of A and B. The sum of the fractions of the tank filled in these two halves must equal 1. We then solve for t.

Step-by-Step Solution:
Step 1: Rate of A = 1/60 tank per minute. Step 2: Rate of B = 1/40 tank per minute. Step 3: In the first half (t/2 minutes), only B works, so fraction filled = (t/2) * 1/40 = t/80. Step 4: In the second half (t/2 minutes), A and B together work, combined rate = 1/60 + 1/40 = (2 + 3) / 120 = 5/120 = 1/24 tank per minute. Step 5: Fraction filled in second half = (t/2) * 1/24 = t/48. Step 6: Total fraction filled = t/80 + t/48 = 1. Take LCM 240: (3t + 5t) / 240 = 8t / 240 = t/30 = 1, so t = 30 minutes.

Verification / Alternative check:
In 15 minutes (half of 30 minutes), B alone fills 15 * 1/40 = 15/40 = 3/8 of the tank. In the next 15 minutes, A and B together fill 15 * 1/24 = 15/24 = 5/8 of the tank. Total = 3/8 + 5/8 = 1 full tank, which confirms the result.

Why Other Options Are Wrong:
31 minutes or 29 minutes: These do not satisfy the equation formed from the rates and lead to a total fraction slightly more or less than 1.
28 minutes: Also fails the rate equation and underestimates the time needed to fill the tanker.

Common Pitfalls:
One common mistake is to assume that the tanker is worked on by both pipes for 30 minutes and then adjusted, rather than defining t properly and splitting it into equal halves. Another pitfall is to add the times instead of adding the fractions of the tank filled. Always work with rates and fractions of work when intervals change.

Final Answer:
The tanker will be filled completely in a total of 30 minutes under the given operating pattern.