Ques:- There is a leak in the bottom of a cistern. When the cisternis thoroughly repaired, it would be filled in 3 ? hours. It now takes half an hour longer. If the cistern is full, howlong will the leak take to empty the cistern?
A. 24 hours
B. 28 hours
C. 21 hours
D. 27 hours
E. None of these
suppose the capacity of cistern is 30unit. when it id repaired
then takes 3 hrs.thus water coming in i hrs=10unit.
now leak tank takes 3 hrs and 1/2 hrs extra. that is, in
general think that the water filling in 1/2 hrs is equal to
the leakage of hole in 3.5 hrs.
leakage in 3.5 hrs is =10/2=5 unit
so 5 unit is leakad in =3.5 hrs
so 30unit(full capacity) is leaked in =3.5*30/5
=21 hrs
so it will take 21 hrs to empty the full cistern.
the answer is 28 hours…….
Time taken to fill repaired cistern = 12 mins
In 1 min, pipe will fill = 1/12
Time taken to fill cistern with leak = 12 + 18 = 30 mins
In 1 min, it will fill = 1/30
Consider the leak as an outlet pipe, so
1/30 = 1/12 – [ in 1 min how much the outlet pipe leaks ]
= 1/12 – 1/30
= 5/60 – 2/60 = 3/60 = 1/20
Therefore, it will take 20 mins for the leak to empty the cistern