a leak in bottom

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Mon Apr 06, 2009 4:21 am

A cistern is filled by an inlet valve in 5 hours. However because of a leak in bottom, it takes 30 minutes more to fill up. In how much time will the leak empty the filled cistern independently?
A. 5.5 hours
B. 55/21 hours
C. 55 hours
D. 11 hours
E. 50 hours

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Source: Beat The GMAT — Problem Solving | Mon Apr 06, 2009 4:21 am

tacosychelas: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Wed Sep 19, 2007 8:06 pmFollowed by: 1 member

by tacosychelas » Mon Apr 06, 2009 4:52 am

C

Formula: Work/Time

1/5 - 1/X = 1/5.5

X=55

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rossmj: Senior | Next Rank: 100 Posts; Posts: 60; Joined: Thu Feb 26, 2009 12:50 pm; Location: Chicago; Thanked: 3 times

by rossmj » Mon Apr 06, 2009 2:20 pm

I get E. 50 hours.

The rate the tank is being filled is 1tank/5hours or 1tank/300min the time is 5.5 hrs or 330 min. So 10% longer than it should have taken. So the rate the tank is leaking would be 1/10th the rate it is being filled or 1tank/3000mins or 1tank/50hours.

Please correct me if I'm wrong and let me know where my logic failed.

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

by logitech » Mon Apr 06, 2009 2:58 pm

tacosychelas wrote:C

Formula: Work/Time

1/5 - 1/X = 1/5.5

X=55

Great solution.

5X=5.5(X-Y)

X=11Y

So 5 hrs vs 55 hrs

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

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dtweah: Master | Next Rank: 500 Posts; Posts: 487; Joined: Fri Mar 27, 2009 5:49 am; Thanked: 36 times

by dtweah » Mon Apr 06, 2009 6:01 pm

tacosychelas wrote:C

Formula: Work/Time

1/5 - 1/X = 1/5.5

X=55

Good soln Logit. For formula or algebra haters just do

1/5 -1/5.5= 1/55. (TAke the difference between per hour work done without and with the leak and you get the per hour work done by the leak)

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