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 un…

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

Wats the answer? Is it 3240 ltrs ?

Let the capacity if the tank be n ltrs. Now the emptying pipe takes n/6 mins or n/360 hours to empty the tank. And the filling pipe takes 6 hours to fill it. So equation for the tank wud be :-

-360/n + 1/6 = 1/18. Solving this, we get n=3240...

@Priyank4 The filling tap would have taken only 6 hours to fill the tank

**without**the leak. But the leak is making it take 3*6=18 hours. Clearly, the effective rate of filling is 1/3rd because of the leak (Rate is always inversely proportional to time taken).So if you take the original rate of filling by the tank as 3x litre per minute, the

*effective*rate of filling*because of the leak*is only x litre per minute. Hence, the rate of leak is 2x litre per min.But 2x = 6, as per the question

=>x = 3.

So the normal rate of filling by the tap is 3x=9 liter per min. Since it takes 6 hours without the leak, the capacity is 9*6 = 54 liters. Let me know if the answer is correct.

@Priyank4 said: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.

ATDH.

@Priyank4

capacity -> x

without leak 6h->x

with leak 18h so 3x

due to leakage 6l lost per min

so per hour is 6*60

in 18 hrs -> 6*60*18

equation becomes : 3x - 360*18 = 2x

which gives x = 3240l

3240 L

@Priyank4 said:@anytomdickandhary Capacity of the tank is 3240 litres

correct hai bhai..... I missed it multiplying it by 60 (to convert hr to minute) in the last step. Hence got 54.

Rest of my steps remain same.

ATDH.

@anytomdickandhary haan wahi bhai i just said ki 3240 sahi answer what u did is also correct ..u just missd dat 60.

@Priyank4 Hmm wo 60 ka factor miss hua, as pointed out above. Hopefully options mein 54 nahi tha? Nahi to galat hota pakka. :P