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# rate problem

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Manager
Joined: 23 Jan 2011
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31 May 2011, 15:26
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(N/A)

Question Stats:

25% (01:02) correct 75% (00:36) wrong based on 7 sessions

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A cold water tube can fulfill a pool in C hours; a hot water tube can fulfill it in H hours. C<H. Two tubes together can fulfill the pool in T hours. Which of the following must be true?

I. 0<T<H
II. C<T<H
III. C/2 < T < H/2

A. I only
B. II Only
C. III Only
D. I and III only
E. I, II and III
Senior Manager
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31 May 2011, 21:42
given C < H.

option 1 - yes ; because T will be less than H. And also C, H and T must be positive.
option 2 - No; because T will be less than values of C and H
option 3 - Yes; because T will be less than values of C and H but 2T will be greater than C and less than H.

these can be proved using example

let C be 2 hrs and H be 3 hrs.
T will be 1/ (1/2 + 1/3) = 6/5 hrs. this satisfies option I and option III.

let C be 40 mins and H be 50 mins.
T will be 1/(1/40 + 1/50) = 200/9 ~ roughly >20 mins
this also satisfies option I and III.

i will go with D.
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31 May 2011, 22:00
My shot is for option D.

Here is why:
This problem can be solved as working-together problem. Let's say, C=5 hours and H=6 hours. If both the tubes are open together, the pool will be filled in (5*6)/(5+6)=2.7 hours(apprx.) i.e. T=2.7 hours. This answer gives validity to options I and III. So, D is the shot.
Then, again, let's say, C=1 hours and H=9 hours. If both the tubes are open together, the pool will be filled in (1*9)/(1+9)=0.9 hours i.e. T=0.9 hours. This answer validates the options I and III, once again. Thus, D is the shot.
(though not necessary anymore) In this way, if you take any positive number, whether faction or integer, answer option I and III will be always valid for this question.
Thank you.
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13 Jun 2011, 01:11
rc = 2 rh = 3,4

t = 6/5 , 4/3.

only A prevails.
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13 Jun 2011, 04:57
amit2k9 wrote:
rc = 2 rh = 3,4

t = 6/5 , 4/3.

only A prevails.

Hi Amit,
Not sure if u meant this :

C= 2 and H = 3.4

1/2+1/3.4= 17/34+10/34 = 27/34
t = 34/27 = 1.26
in this case both 1 and 3 are right .. isnt it?
Re: rate problem   [#permalink] 13 Jun 2011, 04:57
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