A cistern is provided with two pipes A and B. A can fill it in 20 minutes and B can empty it in 30 minutes. If A and B be kept open alternately for one minute each,with starting from pipe A, how soon will the cistern be filled ?

Let the amount of work equivalent to filling a cistern be 60 units

It is given that A pipe takes 20 minutes to fill 60 units,

and B pipe take 30 minutes to empty the tank.

So

A's 1 minute work = 3 units

B's 1 minute of work = -2 units (negative sign is to show that this pipe is emptying the tank)

1st minute, A will fill = 3 units

2nd minute, B will empty = 2 units

So in total 2 minutes, units filled = 3-2 = 1 unit

and hence in 114 minutes only = 57 units will be filled but in 115th minute A will fill the remaining units and so total 115 minutes are required to fill the tank