A tank has a leak at its bottom which empties it at 6 litrs/min. It also has a filling tap which can fill the tank in 6 hours. The tank takes 18 hours to become full. Find the full capacity of the tank .
I have seen its solution even then i am unable to comprehend it so whosoever knows how to do it please tell it with explanation so i that i can understand it .. thank u
okay here are few very simple questions that i present before you which will help you solve this problem without pen and paper.
Q1. if tap also filled water 6lit/min (i.e same at the leakage rate) will the tank ever get filled?
Ans:No. Because the amount of water that is filled in gets leaked out. (Agree??)
Q2: If tap filled water 12lit/min do you agree that after 1 min there would be 6 lit water in tank?
Ans: Yes, Because out of 12 lit filled 6 lit has leaked hence 12-6. i.e effective rate of filling = Filling rate -leakage
Q3:If there was no leakage in the tank, then would the time to fill the tank change if the rate of flow for filling tank was changed?
Ans: Yes, if the fill rate is reduced to half the time will double, and vice versa.
With these simple things clear. We are ready to answer the problem.
Based on question number 3. we can conclude that if the rate of flow is reduced to one third then time to fill the tank would triple. Based on this we conclude that when the leakage is working the effective rate of the filling pipe is reduced to it 1/3rd (thats why it takes 18 hrs rather than 6 hrs).
=>leakage = 2/3 times the filling tap rate
=>6 = 2/3*filling tap rate
=>fill tap rate = 9 lit/min
hence the capacity of the tank = 18*60*(9-6) =3240 lit.