Two taps A and B can fill a cistern in 6 minutes and 12 minutes respectively. The tap C can empty it in 8 minutes. If the three taps are opened simultaneously, then how long will it take to fill the empty cistern.
Answers
Answer:
A cistern has two taps which fill it in 12 minutes and 15 minutes respectively. There is also a waste pipe in the cistern. When all the 3 are opened, the empty cistern is full in 20 minutes.How long will the waste pipe take to empty the full cistern?
Let the 3 taps be A, B and C.
A fills tank in 12 mins -> In 1 min A will fill 1/12 of tank.
B fills tank in 15 mins -> In 1 min B will fill 1/15 of tank.
Lets say C can alone empty the tank in x mins -> In 1 min C will empty 1/x of tank.
According to question, if all taps are opened tank will fill in 20 mins.
In each min 1/20 tank is filled which is due to A, B and C. Now A and B fill the tank will C empty the tank.
1/12 + 1/15 - 1/x = 1/20
1/12 + 1/15 - 1/20 = 1/x
(5+4-3)/60 = 1/x
6/60 = 1/x
x = 10