Question

Pipe a can fill a tank in 2 hours while pipe b can empty the tank in 6 hours. if both the pipes are opened simultaneously, the empty tank can be filled in time ‘t'. ram opened both the pipes and came back to check the tank after time t and found that only 75% tank was filled because pipe a got blocked some time ago. for how long the pipe a had been blocked

Answer 1

pipe a was block 2.25 hour ago

Answer 2

In one hr, 1/2 portion of tank will be filled.
In one hr, 1/6 portion of tank will be emptied.
Thus when operates both, portion of tank filled in one hr will be 1/2 - 1/6 = 1/3.
So tank filled in 3 hrs.

Given that ram checked the tank after 3 hrs. Suppose pipe A blocked after t hrs.
So in t hrs, t/2 portion of tank will be filled.
In 3 hrs, 3/6 portion of tank will be emptied.

Thus when ram came, t/2 - 3/6 portion of tank was filled. This is given as 75%

So, t/2 - 3/6 = 3/4
t = 2.5 hrs