
Shortcut Trick
Total work (LCM of 16, 20) = 80 units.
Efficiency: A = 5, B = 4. 2-hour cycle (A+B) = 9 units.
8 cycles (16 hours) = 9 × 8 = 72 units. Remaining = 80 − 72 = 8 units.
17th hour (Pipe A) fills 5 units. Remaining = 3 units.
Time for B to finish = 3 ÷ 4 = 3/4 hours. Total time = 17 + 3/4 = 17(3/4) hours.
∴ The correct answer is 17(3/4) hours.

Alternate Method
| Person | Days | Total Work | Efficiency |
|---|
| Pipe A | 16 hours | 80 units | 5 |
| Pipe B | 20 hours | 4 | |
Calculation:
⇒ Total capacity of tank = LCM(16, 20) = 80 units.
⇒ Work done in 1st hour (A) = 5 units.
⇒ Work done in 2nd hour (B) = 4 units.
⇒ Work done in 1 cycle (2 hours) = 5 + 4 = 9 units.
⇒ In 8 cycles (16 hours), work done = 9 × 8 = 72 units.
⇒ Remaining work = 80 − 72 = 8 units.
⇒ On 17th hour, Pipe A works and fills 5 units.
⇒ Remaining work after 17 hours = 8 − 5 = 3 units.
⇒ Now it is Pipe B's turn. Time taken by B = 3/4 hours.
⇒ Total time = 17 + 3/4 = 17(3/4) hours.
∴ The correct answer is 17(3/4) hours.

Additional Information
Alternate Work Principle
When pipes work alternatively, calculate the work done in one complete cycle (sum of individual efficiencies) and multiply to reach near the total work.
Pipes & Cisterns Efficiency
Efficiency is inversely proportional to time taken. Total Work = Efficiency × Time. For inlet pipes, efficiency is positive; for outlet pipes, it is negative.