Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 23 May 2015, 02:20

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:
Manager
Joined: 08 Oct 2010
Posts: 213
Location: Uzbekistan
Schools: Johnson, Fuqua, Simon, Mendoza
WE 3: 10
Followers: 9

Kudos [?]: 332 [0], given: 974

There is a leak in the bottom of the tank. This leak can [#permalink]  29 Nov 2010, 00:54
7
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

61% (02:49) correct 39% (02:10) wrong based on 148 sessions
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
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 27465
Followers: 4308

Kudos [?]: 42134 [2] , given: 5957

Re: Work Problem 23 [#permalink]  29 Nov 2010, 01:05
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
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

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: $$8x=12(x-6)$$ --> $$x=18$$ --> $$C=8x=144$$.

Hope it's clear.
_________________
Intern
Joined: 25 Oct 2010
Posts: 18
Followers: 0

Kudos [?]: 2 [2] , given: 1

Re: Work Problem 23 [#permalink]  29 Nov 2010, 02:14
2
KUDOS
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.
Manager
Joined: 30 Aug 2010
Posts: 92
Location: Bangalore, India
Followers: 3

Kudos [?]: 118 [3] , given: 27

Re: Work Problem 23 [#permalink]  29 Nov 2010, 03:14
3
KUDOS
1
This post was
BOOKMARKED
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.

Kudos?
mURALI.
Senior Manager
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 326
Followers: 11

Kudos [?]: 376 [1] , given: 20

Re: Work Problem 23 [#permalink]  13 Jan 2011, 12:24
1
KUDOS
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

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

_________________

press kudos, if you like the explanation, appreciate the effort or encourage people to respond.

Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 17

Kudos [?]: 264 [0], given: 11

Re: There is a leak in the bottom of the tank. This leak can [#permalink]  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

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

Impossible is nothing to God.

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 4922
Followers: 298

Kudos [?]: 54 [0], given: 0

Re: There is a leak in the bottom of the tank. This leak can [#permalink]  23 Dec 2013, 12:08
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Director
Joined: 03 Aug 2012
Posts: 917
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)
Followers: 17

Kudos [?]: 328 [0], given: 322

Re: There is a leak in the bottom of the tank. This leak can [#permalink]  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
_________________

Rgds,
TGC!
_____________________________________________________________________
I Assisted You => KUDOS Please
_____________________________________________________________________________

Director
Status:
Joined: 24 Jul 2011
Posts: 604
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Followers: 76

Kudos [?]: 331 [0], given: 14

Re: There is a leak in the bottom of the tank. This leak can [#permalink]  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).
_________________

GyanOne | http://www.GyanOne.com | +91 9899831738

MBA Section Director
Affiliations: GMAT Club
Joined: 21 Feb 2012
Posts: 1511
Location: India
City: Pune
GPA: 3.4
Followers: 204

Kudos [?]: 1395 [0], given: 1169

Re: There is a leak in the bottom of the tank. This leak can [#permalink]  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.
_________________

Be the coolest guy in the MBA Forum - Be a threadmaster!

Have a blog? Feature it on GMAT Club!

All MBA Resources All 'Sticky' Topics at one place

GMAT Club Premium Membership - big benefits and savings

Next Generation GMATClub CATS with Brilliant Analytics.

Re: There is a leak in the bottom of the tank. This leak can   [#permalink] 18 Mar 2014, 20:46
Similar topics Replies Last post
Similar
Topics:
5 A tank containing water started to leak. Did the tank contai 1 28 Feb 2014, 02:58
A tank containing water started to leak. Did the tank contai 3 23 Feb 2011, 04:12
1 2011 US News Rankings leak? 2 13 Apr 2010, 19:15
1 A 450 gallon water tank is leaking at a rate of 20gallons 1 24 Jul 2006, 14:37
1 Chronic low-level leaking and the routine discharge of 11 26 Oct 2005, 12:05
Display posts from previous: Sort by