An inlet pipe A originating from a river can fill a reservoir in 30 days. And an outlet pipe B, which is capable of emptying the completely filled reservoir in 50 days, drains out the water from the reservoir to an irrigation canal. The pipes are opened on alternate days starting with pipe A. On which day from the beginning will the reservoir get completely filled for the first time?

A = 30 days

B= 50 days

Total work = lcm (30,50)= 150 units

A's efficiency = $$150\div30$$ = 5 units/day

B's efficiency = $$150\div50$$ = -3 units/day (negative sign represents the outlet pipe.)

Work = $$efficiency\times day$$ 

Both pipe together fill 2 units in two day.

so 146 units in 146 days.

After that on 147th-day pipe A will fill the remaining. So in 147 days the reservoir get completely filled for the first time.