A tap can fill an empty cylindrical tank in 5 hours. There are 5 efficient 5 equally leaks at the heights of 0%, 20%, 40%, 60% and 80% of the height of the tank. If the bottom most leak can empty the full tank in 30 hours then what is the time taken to fill the tank?
Answers
here,
a tap can fill a tank in 5 hrs( assuming without a leak)
There are 5 leaks equal and efficient
so, if the leak at 0% can empty the tank in 30hrs
The moment it reaches 20% height the leakage will double up, it'll be triple at 40% and so on till 80%
since a tap can fill the tank in 5 hr
it fills 1/5 of tank in 1 hour
which is also 20%(20/00=1/5) height of the tank
Thus, time taken to fill each 20% height is 1 hour.
tank can leak all the water in 30 hrs
dividing the tank into 5 parts
the time taken to leak is also 30/5= 6hrs
for the first 20% height.
therefore time taken to fill with first leakage= time taken to fill - time taken by leakage
= 1- 1/6 = 5/6 = 1/1.2= 1.2 hrs
2nd leakage = 1-(1/6)×2 (time decreases with each leak, meaning-it'll take less time with each increasing leakage to empty the tank and hence time taken to fill will be more..)
= 1-1/3= 2/3 = 1/1.5= 1.5hrs
3rd leakage= 1- (1/6)3
= 1-1/2= 1/2= 2hrs
4th leakage= 1- (1/6)4
= 1-2/3 = 1/3= 3hrs
5th leakage= 1- (1/6)5
= 1-5/6 = 1/6= 6hrs
Now total time = 1.2+1.5+2+3+6= 13.7 hrs or 13 hrs 42min