Problem Solving

A cistern is filled by an inlet valve in 5 hours. However because of a leak in bottom, it takes 30 minutes more to fill up. In how much time will the leak empty the filled cistern independently?
A. 5.5 hours
B. 55/21 hours
C. 55 hours
D. 11 hours
E. 50 hours

C

Formula: Work/Time

1/5 - 1/X = 1/5.5

X=55

I get E. 50 hours.

The rate the tank is being filled is 1tank/5hours or 1tank/300min the time is 5.5 hrs or 330 min. So 10% longer than it should have taken. So the rate the tank is leaking would be 1/10th the rate it is being filled or 1tank/3000mins or 1tank/50hours.

Please correct me if I'm wrong and let me know where my logic failed.

tacosychelas wrote:C

Formula: Work/Time

1/5 - 1/X = 1/5.5

X=55

Great solution.

5X=5.5(X-Y)

X=11Y

So 5 hrs vs 55 hrs

tacosychelas wrote:C

Formula: Work/Time

1/5 - 1/X = 1/5.5

X=55

Good soln Logit. For formula or algebra haters just do

1/5 -1/5.5= 1/55. (TAke the difference between per hour work done without and with the leak and you get the per hour work done by the leak)