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A rectangular reservoir is filled with water till one-fifth

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Intern
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Joined: 10 Dec 2016
Posts: 21
A rectangular reservoir is filled with water till one-fifth  [#permalink]

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New post 14 Mar 2018, 07:52
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E

Difficulty:

  65% (hard)

Question Stats:

59% (02:17) correct 41% (03:08) wrong based on 30 sessions

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A rectangular reservoir is filled with water till one-fifth of the height of the reservoir. If an outlet at the bottom of the reservoir is unplugged, the water in the reservoir will drain completely in 1 hour. If the outlet remains plugged and the inlet tap at the head of the reservoir is opened, the reservoir will fill to the brim in 2 hours. In how much time will the reservoir fill to the brim if the outlet is unplugged 30 minutes after the inlet tap is opened ?

A) 3 hours

B) 3 hours 30 minutes

C) 4 hours 30 minutes

D) 5 hours

E) The reservoir will never be filled to the brim

Can someone please explain the solution and approach ?
Math Expert
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Joined: 02 Aug 2009
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A rectangular reservoir is filled with water till one-fifth  [#permalink]

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New post 14 Mar 2018, 09:46
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sekharm2389 wrote:
A rectangular reservoir is filled with water till one-fifth of the height of the reservoir. If an outlet at the bottom of the reservoir is unplugged, the water in the reservoir will drain completely in 1 hour. If the outlet remains plugged and the inlet tap at the head of the reservoir is opened, the reservoir will fill to the brim in 2 hours. In how much time will the reservoir fill to the brim if the outlet is unplugged 30 minutes after the inlet tap is opened ?

A) 3 hours

B) 3 hours 30 minutes

C) 4 hours 30 minutes

D) 5 hours

E) The reservoir will never be filled to the brim

Can someone please explain the solution and approach ?



Hi...

1/5 th is filled..
(1) 1 HR to empty it so per HR rate =1/5
(2) 2 HR to fill it completely so (1-1/5=4/5) in 2 hrs..
Full in 2*5/4=5/2, therefore 1 HR wk =2/5..
Combined work = 2/5-1/5=1/5..

Now the reservoir is filled till 1/5. After inlet is on for 1/2 hr, another1/5 is filled since rate is 2/5 in one hour.

So 2/5 is filled when outlet is also opened.
Combined is 1/5, so to do (1-2/5=3/5) work , 3 hrs will be taken..

Total time 30 mins + 3 hrs

B
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A rectangular reservoir is filled with water till one-fifth   [#permalink] 14 Mar 2018, 09:46
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