A tank is normally filled in 18 hours but due to a leak in the bottom, it takes 3 hours more to fill completely. If the tank is filled completely, in what time will the leak empty it completely ?
A). 120 hours
B). 122 hours
C). 124 hours
D). 126 hours
126 hours
Let the time taken by the leak in emptying the tank be 1 hours.
In one hour, the pipe can fill 1/18 part of the tank and the leak can empty 1/x part of the tank.
∴ part of the tank filled in 1 hour
= 1/18 - 1/x = x-18/18x
So, it will be filled completely in
1/(x-18/18x) hours = 18x/x-18 hours
∴ 18x/x-18 = 18 + 3 = 21
or 18x = 21x - 378
∴ x = 378/3 = 126 hours