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# A few taps, numbered 1, 2, 3 . . . , are connected to a tank, each hav

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Math Expert
Joined: 02 Sep 2009
Posts: 47222
A few taps, numbered 1, 2, 3 . . . , are connected to a tank, each hav  [#permalink]

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06 Aug 2017, 00:54
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Difficulty:

15% (low)

Question Stats:

77% (00:41) correct 23% (00:43) wrong based on 69 sessions

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A few taps, numbered 1, 2, 3 . . . , are connected to a tank, each having a distinct rate of filling the tank. What is time taken to fill the tank by the 4th tap alone?

(1) The rate of filling of each tap, starting from the second tap, is double the efficiency of the previous tap.
(2) The time taken by the first five taps, working together, to fill the tank is 1 hour.

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Joined: 24 Apr 2016
Posts: 333
Re: A few taps, numbered 1, 2, 3 . . . , are connected to a tank, each hav  [#permalink]

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06 Aug 2017, 01:35
Let the Rate of $$Tap 1= \frac{1}{R_1}, Tap 2= \frac{1}{R_2}, Tap 3= \frac{1}{R_3}, Tap 4= \frac{1}{R_4}, Tap 5= \frac{1}{R_5}$$

Statement (1) The rate of filling of each tap, starting from the second tap, is double the efficiency of the previous tap.

This statement only gives the relationship between the rates of the different Taps. There is no information related to time. This statement is not sufficient.

Statement (2) The time taken by the first five taps, working together, to fill the tank is 1 hour.

($$\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \frac{1}{R_4} + \frac{1}{R_5}$$) * 1 = 1

As we do not have any further information pertaining to the relationship between the rates of individual taps, this statement is not sufficient.

Combining both the statements we have the relationship between the individual rates, as well as the time taken by the 5 taps together. Using both the statements together is sufficient.

Intern
Joined: 05 Mar 2017
Posts: 3
Re: A few taps, numbered 1, 2, 3 . . . , are connected to a tank, each hav  [#permalink]

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06 Aug 2017, 02:37
Using statement 1: We can assume the efficiency of each tap as x,2x,4x,8x,16x and so on (Geometric Progression).This alone is not sufficient to answer the question.
Statement 2 also doesn't give us anything.But on combining we bot 1 and 2.we get finite GP series and using that we can find x.So the answer will be C.
Re: A few taps, numbered 1, 2, 3 . . . , are connected to a tank, each hav &nbs [#permalink] 06 Aug 2017, 02:37
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