Given: Pipe A can fill in 30 days and pipe B can empty it in 50 days
Pipes are open in an alternate day starting with A
Concept Used: LCM of individual time = Total work
Once the reservoir is filled, work done by the outlet pipe can't be calculated.
Calculation:
Let total work = 150 unit,
When the reservoir will completely fill, last work will be done by pipe A
And the filling was started with pipe A, so in odd days pipe A will open and in even days pipe B will open
Pipe A works on first day, and on the next day pipe B works,
Reservoir fill by Pipe A and pipe B in 2 days = 5 – 3 = 2 unit.
⇒ 146 units reservoir will fill by both pipe in 146 days
In 147th days pipe A will open again and it will fill (146 + 4) = 150 units
∴ In 147th day from the beginning, the reservoir get completely filled for the first time.