There is a leak in the bottom of the tank. This leak can

Another approach:

In 1 hr 1/8th of the tank can be emptied by the leak independently.Let us consider that the tank can be filled in x hrs by the tap independently.In 1 hr 1/x of the tank can be filled.

Net outflow of water in 1 hr is: 1/8 - 1/x = 1/12 (as in 1 hr ,1/12th of tank gets emptied)

==> x = 24hrs(time taken by the tap to fill the tank independently)
==> Total Volume of tank = 24*6 = 144.

Hope this helps.

leak can empty in 8hrs .. but after the inlet was open, it took the leak 12hrs ... so it emptied \(\frac{1}{2}\) extra tank
this means that \(\frac{1}{2}\) tank was basically filled by inlet in 12 hrs
capacity of \(\frac{1}{2}\) tank = 12*6
capacity of full tank = 12*6*2= 144 liters

Let c be the capacity of the full tank.

Let's setup equation of 8 hours to empty full tank = 12 hours to empty tank with tap opened

\(c-8\frac{(c}{8hrs)}=c+(6/hr)(12)-(c/8hr)(12)\)
\(0=c+72-\frac{3c}{2}==>c=144Liters\)

Rate * Time = Work

Rate of inlet = 6 ltr/hour

Rate of outlet = x ltr/hour

Out let pipe work = x * 8 = 8x

So tanks capacity = 8x

Work done by both the pipes is = {Rate of Outlet - Rate of inlet } * Time => (x-6) * 12

Work = (x-6)*12
8x=(x-6)*12

x=18

Capacity = 8*x= 144

The time taken to empty the tank with the inlet tap running increases by 50% from 8 to 12 hours. This means in 12 hours the inlet pumps in water equal to half the tank's capacity. Therefore the tank's capacity = 2 x 6 x 12 = 144L.

Option (C).

We know total water in the tank, when it is full, is 100%

Leak can empty a full tank in 8 hr. -----------> Leak is emptying \(\frac{100}{8}\) i.e. 12.5% tank in one hour. ----------> Stat I

Tap intakes water at rate of 6 liter per hr. Lets assume tap can fill P% tank in one hour ------------ Stat II

Tank is now emptied in 12 hr. ---------> 100/12 ----> 8.33% Tank is now emptied in one hour.

Using Statement I and II we have that 8.33 = 12.5 - P% -------> P% = 4.17%

We know Tap is filling 6 liters per hour. We also know tap is filling 4.17% of the tank in on hour. That means 6 liter = 4.17% of tank's total capacity, so tanks total capacity is \(\frac{6*100}{4.17}\) OR 144 liters.

Let the capacity of the tank be = V ltrs
Time taken to empty a full tank- 8 hr

The rate of emptying the tank is = V/8 lts/hr
The rate of filling the tank = 6 lts/hr

Net rate = [ (V/8)- 6] lts/hr
new time taken to empty the tank = 12 hr

net Rate x time = Capacity of the tank

[ (V/8)- 6] x 12 = V
V= 144 lts (ans.)

Here's my solution,
Let x be the capacity of the tank, the tap fills 12×6=72 litres.
So, x/x+72 : 8/12
3x - 2x = 144,
Hence, C

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There is a leak in the bottom of the tank. This leak can empty a full tank in 8 hr. When the tank is full, a tap is opened into the tank which intakes water at rate of 6 liter per hr. and the tank is now emptied in 12 hr. What is the capacity of the tank?

12 ( x - 6) = 8x
12x - 72 = 8x
72 = 4x
x = 18
8x = 144

We can PLUG IN THE ANSWERS, which represent the capacity of the tank.
When the correct answer is plugged in, the time for the leak and the tap together to empty the tank = 12 hours.
Since all of the values in the prompt are INTEGERS, the correct answer is almost certain to be a multiple of the given integer values.
Only C is divisible by 8, 6 and 12.

C: 144 liters
Since the leak takes 8 hours to empty the 144-liter tank, the rate for the leak \(= \frac{work}{time} = \frac{144}{8} = 18\) liters per hour.
Since the leak EMPTIES at a rate of 18 liters per hour, while the tap INPUTS at a rate of 6 liters per hour, the emptying rate for the leak and the tap together = 18-6 = 12 liters per hour.
Since their combined rate = 12 liters per hour, the time for the leak and the tap together to empty the 144-liter tank \(= \frac{work}{rate} = \frac{144}{12} = 12\) hours.
Success!

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