Shortcut Trick
Total Work (LCM of 20, 35) = 140 units.
Efficiency: X = 7, Y = 4. 2-hour cycle (Y + X) = 4 + 7 = 11 units.
12 cycles (24 hours) = 12 × 11 = 132 units. Remaining = 140 − 132 = 8 units.
25th hour (Pipe Y): 4 units filled. Remaining = 4 units. Time for X = 4/7 hours.
Total Time = 24 + 1 + 4/7 = 25 + 4/7 = 179/7 hours.
∴ The correct answer is 179/7 hours.
Alternate Method
| Pipe | Time (hrs) | Total Work | Efficiency |
|---|
| X | 20 | 140 | 7 |
| Y | 35 | 4 | |
⇒ Total Capacity = LCM(20, 35) = 140 units.
⇒ Efficiency of X = 140 ÷ 20 = 7 units/hr.
⇒ Efficiency of Y = 140 ÷ 35 = 4 units/hr.
⇒ Since they work on alternate hours starting with Y:
⇒ Work in 1st hour (Y) = 4 units; Work in 2nd hour (X) = 7 units.
⇒ Total work in 2 hours = 4 + 7 = 11 units.
⇒ Work done in 12 such cycles (24 hours) = 12 × 11 = 132 units.
⇒ Remaining work = 140 − 132 = 8 units.
⇒ On 25th hour, Y fills 4 units. Remaining = 8 − 4 = 4 units.
⇒ Time taken by X to fill last 4 units = 4/7 hours.
⇒ Total time = 24 + 1 + 4/7 = 179/7 hours.
∴ The correct answer is 179/7 hours.
Additional Information
Alternate Day/Hour Concept
In alternate work, tasks are calculated in cycles. The order of pipes/workers significantly changes the total time if the work is not a perfect multiple of the cycle's total efficiency.
Pipes and Cisterns
Efficiency is inversely proportional to time. Filling pipes have positive efficiency, while leakage or outlet pipes have negative efficiency.