# In How Much Time Tank will be Filled. If A, B and C are Opened Successively for a Minute Each.

Two pipes A and B can separately fill a tank in 20minutes and 30minutes respectively while a third pipe C can empty it in 15 minutes. If A, B and C are opened successively for a minute each, the tank will be filled in

1. 60 minutes
2. 58 minutes
3. 172 minutes
4. 180 minutes

Explanation:-
Pipe A can fill a tank = 20 minutes
Therefore, A can fill a tank in a minute = 1/20

Pipe B can fill a tank = 30 minutes
Therefore, B can fill a tank in a minute = 1/30

Pipe C can empty it = 15 minutes
Therefore, C can empty it in a minute = 1/15

A, B and C are opened = 1/20 + 1/30 – 1/15
= (3 + 2 – 4)/60
= 1/60

1/60 of a tank filled in 3 minutes,
Therefore,  [1 – (1/20 + 1/30)]
= 55/60
55/60 of a tank filled in 3 x 55 minutes
Now, 5/60 of the tank  remains to be filled.
A will fill 1/20  in 1 minute and B  will fill the remaining
= (5/60 – 1/20)
= 1/30 in 1 minute
Therefore, time required = 165 + 1 + 1 + 5
= 172 minutes

Hence, the answer is (3) 172 minutes.