Pipes and Cisterns

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coolhabhi: Master | Next Rank: 500 Posts; Posts: 141; Joined: Tue Oct 04, 2011 5:17 am; Thanked: 25 times

by coolhabhi » Thu Jan 05, 2017 11:47 am

A tap takes 36 hours extra to fill a tank due to a leakage equivalent to half of its inflow. The inlet pipe alone can fill the tank in how many hours?
(1) 18
(2) 24
(3) 30
(4) 36
(5) 40

OE: A

I have been banging my head to solve this problem but I am unable to. Could the experts please help me out.

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Source: Beat The GMAT — Problem Solving | Thu Jan 05, 2017 11:47 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Jan 05, 2017 12:10 pm

coolhabhi wrote:A tap takes 36 hours extra to fill a tank due to a leakage equivalent to half of its inflow. The inlet pipe alone can fill the tank in how many hours?
(1) 18
(2) 24
(3) 30
(4) 36
(5) 40

Let t = the normal time.

Since 1/2 the inflow is lost, the normal inflow rate is cut in 1/2.
Rate and time have a RECIPROCAL RELATIONSHIP.
HALF the normal rate implies TWICE the normal time.
Since twice the normal time is equal to 36 more hours than the normal time, we get:
2t = 36 + t
t = 36.

The correct answer is D.

Your source is incorrect if it lists A as the OA.

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Thu Jan 05, 2017 6:36 pm

Hi coohhabhi,

Since the answer choices to this question are numbers, we can TEST THE ANSWERS. We're told that it takes 36 EXTRA hours for a tap to fill a tank because of a leak that is releasing HALF of the water that's coming in. We're asked how long it would normally take the tap to fill the tank.

Let's TEST Answer D: 36 hours....

If it would normally take 36 hours to fill a tank BUT there's a leak that's releasing half of the inflow, then it should take TWICE as long to fill the tank as normal. Thus, instead of 36 hours, it would take 72 hours to fill the tank. That's a difference of 72 - 36 = 36 extra hours. This matches what we were told, so this MUST be the answer.

Final Answer: D

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Rich

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Tue Jan 10, 2017 10:52 pm

coolhabhi wrote:A tap takes 36 hours extra to fill a tank due to a leakage equivalent to half of its inflow. The inlet pipe alone can fill the tank in how many hours?
(1) 18
(2) 24
(3) 30
(4) 36
(5) 40

OE: A

I have been banging my head to solve this problem but I am unable to. Could the experts please help me out.

Say the inlet pipe alone can fill the tank in x hours, thus, the leakage alone can empty the tank in 2x hours.

When the inlet pipe and the leakage were in operation, it took (x+36) hours to fill the tank.

Thus,

1/x - 1/(2x) = 1/(x+36)

=> 1/(2x) = 1/(x+36)

=> 2x = x+36

=> x=36 hours. It would take the inlet pipe alone to fill the tank in 36 hours.

Answer: D

-Jay
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