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

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There is a leak in the bottom of the tank. This leak can [#permalink] New post 29 Nov 2010, 00:54
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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 inteks water at rate of 6 liter per hr. and the tank is now emptied in 12 hr. What is the capacity of the tank?

A. 28.3 liter
B. 36 liter
C. 144 liter
D. 150 liter
E. cannot be determined
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Re: Work Problem 23 [#permalink] New post 29 Nov 2010, 01:05
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feruz77 wrote:
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 inteks water at rate of 6 liter per hr. and the tank is now emptied in 12 hr. What is the capacity of the tank?

a) 28.3 liter
b) 36 liter
c) 144 liter
d) 150 liter
e) cannot be determined

Pls. your solution methods?
I think there must more than one solution method!
My appreciations and KUDOS for detailed explanation !!!


Let the rate at which the leak empties the tank be x liter per hour. Then the capacity of the tank will be C=time*rate=8x;

Now, when the tap into the tank with the rate of 6 liter per hour is opened the net outflow is decreased to x-6 liter per hour, and we are told that at this new rate the tank is emptied in 12 hours. So, the capacity of the tank also equals to C=time*rate=12(x-6);

Thus we have: 8x=12(x-6) --> x=18 --> C=8x=144.

Answer: C.

Hope it's clear.
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Re: Work Problem 23 [#permalink] New post 29 Nov 2010, 02:14
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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.
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Re: Work Problem 23 [#permalink] New post 29 Nov 2010, 03:14
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Let me try to put the solution with out using any variables such as x, y....etc.

. At the start of the process the tank was FULL
. a tap gives 6 liters water per hour.
. the tank is emptied in 12 hours

==> means, the tap was run for 12 hours and hence contributed 12*6 = 72 liters of water.

the leak can empty the ful tank tank in 8 hours. and the tank was intially full.

but it took 12 hours (4 extra hours) for the leak to empty the tank.....
qtn: what is the factor that caused the leak to take these 4 extra hours to empty the tank......YES, nothing but the tap which produced 72 liters of water.

hence, in those 4 hours the leak emptied 72 liters
==> in 8 hours it can empty 72*2 =144 liters
and as we know the leak can EMPTY THE WHOLE CAPACITY IN 8 HOURS==> THE CAPACITY OF THE TANK MUST BE 144 LITERS.

Regards,
Murali.

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Re: Work Problem 23 [#permalink] New post 13 Jan 2011, 12:24
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feruz77 wrote:
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 inteks water at rate of 6 liter per hr. and the tank is now emptied in 12 hr. What is the capacity of the tank?

a) 28.3 liter
b) 36 liter
c) 144 liter
d) 150 liter
e) cannot be determined

Pls. your solution methods?
I think there must more than one solution method!
My appreciations and KUDOS for detailed explanation !!!


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

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Re: There is a leak in the bottom of the tank. This leak can [#permalink] New post 16 Nov 2012, 00:43
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
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Re: There is a leak in the bottom of the tank. This leak can [#permalink] New post 23 Dec 2013, 12:08
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Re: There is a leak in the bottom of the tank. This leak can [#permalink] New post 18 Mar 2014, 05:34
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
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Re: There is a leak in the bottom of the tank. This leak can [#permalink] New post 18 Mar 2014, 11:39
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).
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Re: There is a leak in the bottom of the tank. This leak can [#permalink] New post 18 Mar 2014, 20:46
Expert's post
feruz77 wrote:
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?

A. 28.3 liter
B. 36 liter
C. 144 liter
D. 150 liter
E. cannot be determined


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.
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Re: There is a leak in the bottom of the tank. This leak can   [#permalink] 18 Mar 2014, 20:46
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