Pipes A and B can fill a cistern in 20 min and 30 min and C can empty it in 15 min. If the three are kept open successively for 1 min each in the order how soon will the cistern be filled?

a) 180min b) 90min c) 120 min d) 60 min

Answer is : A

Solution :

Given :-
1. A fills in                 => 20 min
2. B fills in                 => 30 min
3. C can empty in      => 15 min

What To Find:- 
How much time will it take to fill the cistern if we use each for one minute in order one by one?

Procedure :-
1. in 1 minute A can be fill = 1/20th part
2. in 1 minute B can be fill = 1/30th part
3. in 1 minute C can be fill = -1/15th part

So,
for first 3 minutes A, B and C can fill  = 1/20 + 1/30 - 1/15 = 1/60
=> In 3 minutes A+B+C can  be  fill   = 1/60th Part.
=> Time taken to fill  1/60 part          =  3 min
=> Time taken to fill full part             =  3 * 60 min = 180 minutes.


(Note :- in Problem it is clear that  first 

      A will be opened for 1 min and then

      B opened for 1 minute and then 

      C opened for 1 minute 

      and again A,B and then C and so on......

So for first 3 minutes A, B and C will be Opened each for one minute)