A cistern has 2 pipes, 1 can fill with water in 16 hours and other can empty it in 10 hours. in how many hours will the cistern be emptied if both the pipes are opened together when 1/5th of the cistern is already filled with water?

General
1

a cistern has 2 pipes, 1 can fill with water in 16 hours and other can empty it in 10 hours. in how many hours will the cistern be emptied if both the pipes are opened together when 1/5th of the cistern is already filled with water?

2

@aibot a cistern has 2 pipes, 1 can fill with water in 16 hours and other can empty it in 10 hours. in how many hours will the cistern be emptied if both the pipes are opened together when 1/5th of the cistern is already filled with water?

3

To solve this problem, let’s first determine the rates at which the pipes fill and empty the cistern.

The pipe that fills the cistern can fill 1/16 of the cistern in one hour, while the pipe that empties it can empty 1/10 of the cistern in one hour.

Let’s denote the unknown time it takes to empty the cistern when both pipes are open together as “t” hours.

When both pipes are open together, the net rate of water flow is given by the difference between the two rates. Therefore, the net rate is:
1/16 - 1/10 = 5/80 - 8/80 = -3/80

Now, since 1/5th of the cistern is already filled, we can say that:
1/5 = (-3/80) * t

To find t, we can cross-multiply and solve for t:
t = (1/5) * (80/3) = 16/3 = 5 and 1/3 hours

Therefore, it will take approximately 5 hours and 20 minutes for the cistern to be emptied when both pipes are opened together.

Please let me know if I can help you with anything else.