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Machine M, N, O working simultaneously Machine M can produce

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Machine M, N, O working simultaneously Machine M can produce [#permalink] New post 26 Aug 2011, 06:30
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Machine M, N, O working simultaneously Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 2/3 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?

A. 1/2
B. 1/3
C. 4/13
D. 8/29
E. 6/33


[Reveal] Spoiler: Solution
N produces x units in ‘t’
M produces x units in ¾ t
O produces x units in 3/2t

In 1 minute total units produced by M,N,O working together = 1/t + 4/3t + 2/3t = 3/t
Ratio of work done by N in 1 minute = (1/t) / (3/t) = 1/3
This ratio will be the same no matter how long M, N, O work together.
[Reveal] Spoiler: OA

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Re: machines m,n,o working simaltaneously [#permalink] New post 07 Mar 2012, 08:17
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MBAhereIcome wrote:
Machine M,N,O working simultaneously Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 2/3 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?

A. 1/2
B. 1/3
C. 4/13
D. 8/29
E. 6/33


Think in terms of ratios for a quick clean solution.
Time taken by M : time taken by N = 3:4
So speed of M : speed of N = 4:3
Similarly, speed of N:speed of O = 3:2
Speed of M: Speed of N : Speed of O = 4:3:2
So N will produce 3/(2+3+4) = 1/3rd of the output
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Re: machines m,n,o working simaltaneously [#permalink] New post 26 Aug 2011, 06:47
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MBAhereIcome wrote:
Machine M,N,O working simultaneously Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 2/3 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?

A. 1/2
B. 1/3
C. 4/13
D. 8/29
E. 6/33


[Reveal] Spoiler: Solution
N produces x units in ‘t’
M produces x units in ¾ t
O produces x units in 3/2t

In 1 minute total units produced by M,N,O working together = 1/t + 4/3t + 2/3t = 3/t
Ratio of work done by N in 1 minute = (1/t) / (3/t) = 1/3
This ratio will be the same no matter how long M, N, O work together.


Okieee..

Now ultimately the speed of every machine is given with respect to Mach O.
So lets assume the speed of O, say 12 hrs to make x units (assuming 6 because we can see we will need to divide by 3 and 4

Mach O makes x units in 12 hrs
So, Mach N = 2/3 of O = 2/3*12 = 8 hrs to make x units
and Mach M = 3/4 of N = 3/4*8 = 6 hrs to make x units

No they are running simultaneously. Lets see how much each mach makes in 1 hr
Mach O = x/12 units
Mach N = x/8 units
Mach M = x/6 units

In 1 hr, together they make - x/12+x/8+x/6 = 3x/8
So what ratio of this has Mach N made?

(x/8) / (3x/8) = 1/3

Ans: B=1/3
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Re: machines m,n,o working simaltaneously [#permalink] New post 04 Oct 2011, 11:25
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Work done by O = 1/O
Work Done by N = 1/N = 1/(2/3)O = 3/2O

Work done by M = 1/M = 1/(3/4)N = 1/(3/4)(3/2O) = 12 /6 O = 2 /O

Worn done y N = 1/O + 3/2 O + 2/O = 2 + 3 + 4 / 2O = 9 /2O
= 1/3 part of whole work done
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Re: machines m,n,o working simaltaneously [#permalink] New post 04 Oct 2011, 11:38
@MBAhereIcome - Kudos to you for this excellent question.

Answer is B. Cheers!
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Re: machines m,n,o working simaltaneously [#permalink] New post 07 Mar 2012, 08:04
Let O --> T = 12 hours to finish the job
Let N --> N = \frac{2}{3}*T = 8 hours the job
Let M --> M = \frac{3}{4}*\frac{2}{3} * T = 6 hours to finish the job
Combine their rates: \frac{1}{6}+\frac{1}{8}+\frac{1}{12} = \frac{3}{8} Rate to finish one job together
We are looking for the fraction of N on the whole output.
Rate of N is \frac{1}{8}, multiply it with the total time of all machines *\frac{8}{3} = \frac{1}{3}

Hope its correct. Took me 10 minutes :|
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Re: machines m,n,o working simaltaneously [#permalink] New post 11 Mar 2012, 16:26
I know we are supposed to say thank you by just pressing kudos but I must add here that your methods are very efficient.


VeritasPrepKarishma wrote:
MBAhereIcome wrote:
Machine M,N,O working simultaneously Machine M can produce x units in 3/4 of the time it takes machine N to produce the same amount of units. Machine N can produce x units in 2/3 the time it takes machine O to produce that amount of units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?

A. 1/2
B. 1/3
C. 4/13
D. 8/29
E. 6/33


Think in terms of ratios for a quick clean solution.
Time taken by M : time taken by N = 3:4
So speed of M : speed of N = 4:3
Similarly, speed of N:speed of O = 3:2
Speed of M: Speed of N : Speed of O = 4:3:2
So N will produce 3/(2+3+4) = 1/3rd of the output
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Re: Machine M, N, O working simultaneously Machine M can produce [#permalink] New post 20 Sep 2013, 09:07
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Re: Machine M, N, O working simultaneously Machine M can produce [#permalink] New post 14 Mar 2014, 12:59
I would go with smart numbers on this one. Say that N=4, M=3 and O = 6. Therefore all working together will finish x in 4/3 hour. Now in 4/3 hour N does 1/4 so (4/3)(1/4) = 1/3. B is the correct answer

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Re: Machine M, N, O working simultaneously Machine M can produce   [#permalink] 14 Mar 2014, 12:59
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