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A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Eac

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A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Eac  [#permalink]

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New post Updated on: 24 Apr 2015, 08:36
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A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Each of the three narrow pipes works at 1/2 the rate of each of the wide pipes. All the pipes working together will take what fraction of time taken by the two wide pipes working together to fill the tank?

(A) 1/2
(B) 2/3
(C) 3/4
(D) 3/7
(E) 4/7

Originally posted by GMATPASSION on 23 Sep 2011, 01:16.
Last edited by Bunuel on 24 Apr 2015, 08:36, edited 1 time in total.
Renamed the topic and edited the question.
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Re: A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Eac  [#permalink]

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New post 05 May 2015, 00:45
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5
The question plays on the concept that time taken to do a work is inversely proportional to the rate of doing the work. We can deduce this relation from the expression

Work = Rate * Time i.e. Time = Work/Rate.

If the work done by two entities are the same, the ratio of time taken by them would be the inverse ratio of their rate of doing work.

Given:
The question gives us the relation between the rates of the wide and narrow pipes and asks us to find the ratio of time taken by all pipes working together to that of only wide pipes working together for filling up the tank.

Approach
The work done by all pipes working together and only wide pipes working together is the same i.e. filling the tank. As the work to be done is same, the ratio of time taken will be inversely proportional to the rate.So, inverting the ratio of rates would gives us the ratio of time. Let's see what information has been given to us about the rates of the pipes.

Working Out:
We are told that rate of work done by wide pipe is double the rate of work done by narrow pipe. If we assume the rate of narrow pipe to be r, the rate of wider pipe would be 2r.

We are asked to find (Time taken by all the pipes)/(Time taken by two wide pipes) = (Rate of two wide pipes)/ (Rate of all the pipes)=\(\frac{( 2r + 2r)}{( r +r + r +2r +2r)} = \frac{4}{7}\) which is our answer.

Takeaway
For time and work question, remember the relation between the work, time and rate for a set of different entities:

a. Greater the rate of doing work, lesser the amount of time taken, assuming the work done to be constant
b. Greater the amount of time taken, lesser the rate of doing work, assuming the work done to be constant
c. Greater the amount of time taken, greater the amount of work done, assuming the rate to be constant
d. Greater the rate of doing work, greater the amount of work done, assuming time taken to be constant


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Re: A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Eac  [#permalink]

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New post 23 Sep 2011, 01:29
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GMATPASSION wrote:
A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Each of the three narrow pipes works at 1/2 the rate of each of the wide pipes. All the pipes working together will take what fraction of time taken by the two wide pipes working together to fill the tank?

(A) 1/2
(B) 2/3
(C) 3/4
(D) 3/7
(E) 4/7

Different ways of doing this question will be highly appreciated.


I always plug in for these questions.. I find them easier

Let 2 large pipes each work fill 10lts/hr
small ones = 1/2*10 = 5
total 5 = 10+10+5+5+5 = 35 lts/hrs

now assume the total capacity = 140 lts ( LCM of 20,35)

Qn :All the pipes working together will take what fraction of time taken by the two wide pipes working together to fill the tank

all working together will take 140/35 = 4 hrs
two large pipes working will take 140/20 = 7 hrs

hence ratio = 4/7 = E
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Re: A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Eac  [#permalink]

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New post 23 Sep 2011, 01:33
@ Sudhir

Gr8 solution. That LCM part was really awesome.Looking forward for some gr8 solution from other members. :)
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Re: A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Eac  [#permalink]

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New post 23 Sep 2011, 11:30
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I answered this in a similar way with a different twist...

Narrow = 3; Wide = 2;

Assume each Wide = 10 liters per hour (10 l/hr)
Assume each narrow = 10*0.5 = 5 liters per hour (5 l/hr)

Wide total work = 2*10 l/hr = 20 liters per hour
Total work = 3*5 + 2*10 = 35 liters per hour

ratio of work = 35/20 = 7/4
W = R*t ---> Time is just the inverse of Work rate ---> 4/7...
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Re: A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Eac  [#permalink]

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New post 23 Sep 2011, 20:55
8
3
Another approch without plugging in:

Let the wide pipe's rate be : x
Let the thin pipe's rate be : x/2

Formula: Speed * time= work
Eq1 : speed of all pipes together * T1 = W (Work is going to be constant)
Total speed: 3(x/2) + 2x = 7x/2
7x/2 * T1 = W

Eq2: Speed of 2 wide pipes only * T2 = W
Total speed: 2x
2x * T2 = W

The expectation is to find out T1/T2= 4/7
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A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Eac  [#permalink]

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New post 25 Jun 2015, 10:32
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GMATPASSION wrote:
A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Each of the three narrow pipes works at 1/2 the rate of each of the wide pipes. All the pipes working together will take what fraction of time taken by the two wide pipes working together to fill the tank?

(A) 1/2
(B) 2/3
(C) 3/4
(D) 3/7
(E) 4/7



I'm sure the long responses are meant to help explain the solution. I want to stress that the answer should be a simplistic as possible, without losing quality, of course. The approach I went with is below:

\(\frac{w}{2}\) = small pipe
w = wide pipe

Total flow: \(\frac{w}{2} * 3 +2w = \frac{7}{2}w\)
Ratio of flows: \(\frac{7w}{2} : 2w = 7:4\)
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Re: A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Eac  [#permalink]

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New post 27 Sep 2016, 01:56
1
Let wide pipe rate = 6
smaller pipe rate = 3

total rate of all pipes working together = 3[1/6] + 2[1/3] = 7/6
rate of wide pipes = 2/3

[2/3] / [7/6] = 4/7
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Re: A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Eac  [#permalink]

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New post 11 Apr 2017, 16:17
sudhir18n wrote:
GMATPASSION wrote:
A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Each of the three narrow pipes works at 1/2 the rate of each of the wide pipes. All the pipes working together will take what fraction of time taken by the two wide pipes working together to fill the tank?

(A) 1/2
(B) 2/3
(C) 3/4
(D) 3/7
(E) 4/7

Different ways of doing this question will be highly appreciated.


I always plug in for these questions.. I find them easier

Let 2 large pipes each work fill 10lts/hr
small ones = 1/2*10 = 5
total 5 = 10+10+5+5+5 = 35 lts/hrs

now assume the total capacity = 140 lts ( LCM of 20,35)

Qn :All the pipes working together will take what fraction of time taken by the two wide pipes working together to fill the tank

all working together will take 140/35 = 4 hrs
two large pipes working will take 140/20 = 7 hrs

hence ratio = 4/7 = E


Hi Sudhir,

I have a small doubt.

In the solution, till the below line I understood

time taken by all pipes together : time taken by 2 wide pipes=4:7

but in question we are asked for the fraction, why did we not make it 4/11?

I guess there is a gap in my understanding. Please help !
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Re: A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Eac  [#permalink]

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New post 11 Apr 2017, 21:34
AR15J wrote:
Hi Sudhir,

I have a small doubt.

In the solution, till the below line I understood

time taken by all pipes together : time taken by 2 wide pipes=4:7

but in question we are asked for the fraction, why did we not make it 4/11?

I guess there is a gap in my understanding. Please help !


Because the time taken by two large pipes is already accounted in 7.
7 actually consists of 4(time taken by large pipes) and 3(time taken by small pipes).

Hope its clear..
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Re: A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Eac  [#permalink]

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New post 25 Apr 2017, 10:21
sudhir18n wrote:
GMATPASSION wrote:
A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Each of the three narrow pipes works at 1/2 the rate of each of the wide pipes. All the pipes working together will take what fraction of time taken by the two wide pipes working together to fill the tank?

(A) 1/2
(B) 2/3
(C) 3/4
(D) 3/7
(E) 4/7

Different ways of doing this question will be highly appreciated.


I always plug in for these questions.. I find them easier

Let 2 large pipes each work fill 10lts/hr
small ones = 1/2*10 = 5
total 5 = 10+10+5+5+5 = 35 lts/hrs

now assume the total capacity = 140 lts ( LCM of 20,35)

Qn :All the pipes working together will take what fraction of time taken by the two wide pipes working together to fill the tank

all working together will take 140/35 = 4 hrs
two large pipes working will take 140/20 = 7 hrs

hence ratio = 4/7 = E
thanks for the explanation :-D
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Re: A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Eac  [#permalink]

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New post 25 Apr 2017, 10:44
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GMATPASSION wrote:
A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Each of the three narrow pipes works at 1/2 the rate of each of the wide pipes. All the pipes working together will take what fraction of time taken by the two wide pipes working together to fill the tank?

(A) 1/2
(B) 2/3
(C) 3/4
(D) 3/7
(E) 4/7


We know rates are additive so let's work with rates. We will convert it to time later.
Say rate of work of each narrow pipe is R. So rate of work of each wide pipe is 2R.

Rate of work of two wide pipes = 2*2R = 4R
Rate of work of all 5 pipes = 3R + 4R = 7R

Ratio of rate of work of all 5 pipes: 2 wide pipes = 7:4
Rati of time taken by all 5 pipes: 2 wide pipes = 4:7

So all 5 pipes take 4/7 of the time taken by 2 wide pipes alone.

For more, check: https://www.veritasprep.com/blog/2011/0 ... -problems/
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A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Eac  [#permalink]

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New post Updated on: 16 Sep 2018, 15:46
GMATPASSION wrote:
A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Each of the three narrow pipes works at 1/2 the rate of each of the wide pipes. All the pipes working together will take what fraction of time taken by the two wide pipes working together to fill the tank?

(A) 1/2
(B) 2/3
(C) 3/4
(D) 3/7
(E) 4/7


let combined rate of 2 wide pipes=2*2=4
combined rate of 3 narrow pipes=3*1=3
time for all 5 pipes=1/(4+3)=1/7
time for 2 wide pipes=1/4
(1/7)/(1/4)=4/7
E

Originally posted by gracie on 25 Apr 2017, 14:27.
Last edited by gracie on 16 Sep 2018, 15:46, edited 1 time in total.
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Re: A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Eac  [#permalink]

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New post 16 Sep 2018, 13:50
GMATPASSION wrote:
A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Each of the three narrow pipes works at 1/2 the rate of each of the wide pipes. All the pipes working together will take what fraction of time taken by the two wide pipes working together to fill the tank?

(A) 1/2
(B) 2/3
(C) 3/4
(D) 3/7
(E) 4/7


\(5\,\,{\text{pipes}}\,\,\,\left\{ \begin{gathered}
\,3\,\,{\text{narrow}}\,\,\,\, \to \,\,\,{\text{each}}\,\,\,1\,\,{\text{gallons}}/\min \,\,\, \hfill \\
\,2\,\,{\text{wide}}\,\,\,\,\,\,\,\,\, \to \,\,\,{\text{each}}\,\,\,2\,\,{\text{gallons}}/\min \hfill \\
\end{gathered} \right.\,\,\,\,\,\left( {{\text{particular}}\,\,{\text{case}}!} \right)\)

\({\text{A}}\,\,\,{\text{ = }}\,\,\,{\text{2}}\,\,{\text{wide}}\,\,{\text{together}}\,\,\,{\text{:}}\,\,\,\,2 \cdot 2 = 4\,\,{\text{gallons/min}}\)

\({\text{B}}\,\,\,{\text{ = }}\,\,\,{\text{all}}\,\,{\text{5}}\,\,{\text{together}}\,\,\,{\text{:}}\,\,\,\,3 \cdot 1 + 2 \cdot 2 = 7\,\,{\text{gallons/min}}\)

\({\text{B:A}}\,\,\underline {{\text{work}}} \,\,{\text{ratio}}\,\,\left( {{\text{per}}\,\,{\text{any}}\,\,{\text{time}}} \right)\,\,\,{\text{ = }}\,\,\,\,\frac{7}{4}\,\,\,\,\,\)

\(?\,\,\, = \,\,\,B:A\,\,\underline {{\text{time}}} \,\,{\text{ratio}}\,\,\,\left( {{\text{per}}\,\,{\text{any}}\,\,{\text{work}}} \right)\,\,\, = \,\,\,{\left( {\frac{7}{4}} \right)^{ - 1}} = \,\,\,\frac{4}{7}\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
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Re: A tank has 5 inlet pipes. Three pipes are narrow and two are wide. Eac   [#permalink] 16 Sep 2018, 13:50
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