Pipe A can fill a tank in 3 hours. But there is a leakage also, due to which it takes 3.5 hours, for the tank to be filled. How much time will the leakage take in emptying the tank if the tank is filled initially?
We are going to use the fact that efficiency is inversely proportional to the time taken i.e. more is the efficiency, lesser is the time taken to complete the job.
So. since the pipe can fill the tank in 3 hours, its efficiency = 1 / 3 = 100 / 3 % = 33.33%
Now, let the emptying efficiency be = x %
So, total efficiency = (33.33 - x) % = (33.33 - x) / 100
Now, no. of hours taken to fill the tank (that is complete the work) = reciprocal of the total efficiency
= 100 / (33.33 - x)
Also, since it takes 3.5 hours to fill the tank, we have
100 / (33.33 - x) = 3.5
⇨ 1000 / 35 = 33.33 - x
⇨ x = (33.33 - 28.57) % = 4.76 % = 4.76 / 100
So, now we have the emptying efficiency = 4.76 / 100
Therefore, the time taken to empty the tank is inverse of emptying efficiency = 100 / 4.76
= 21 hours
The correct option is D.