Question

A pipe can fill a tank completely in 10
hours but it takes
2 hours more due to a
leak. If a second pipe which is half the
efficiency of the first one is opened and
the first pipe is closed, in how much time
will the second pipe along with the leak be
able to fill half the tank?​

Answer 1

TIME TAKES BY THE PIPE TO FILL THE TANK = 10hrs

PART OF THE TANK FILLED BY THE PIPE IN 1 HOUR = 1/10

LET THE TIME TAKEN BY THE LEAK TO EMPTY THE FULL TANK BE = X

PART OF THE TANK EMPTIED BY THE LEAK IN 1 HOUR = 1/X

TIME TAKEN TO FILL THE TANK = 20 HOURS.

PART OF THE TANK FILLED IN 1 HOUR = 1/20

1/10–1/X = 1/20

(X-10)/10X = 1/20

X-10 = 10X/20

X - 10 = X/2

X-X/2 = 10

X/2 = 10

X= 2x10 = 20

TIME TAKEN BY THE LEAK TO EMPTY THE TANK = 20 HOURS