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Machine M, N, O working simultaneously Machine M can produce [#permalink]

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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?

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.

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]

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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?

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 _________________

Happy Learning ! :D

Show Thanks to fellow members with Kudos its shows your appreciation and its free

Re: machines m,n,o working simaltaneously [#permalink]

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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]

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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 \(*\frac{8}{3} = \frac{1}{3}\)

Re: machines m,n,o working simaltaneously [#permalink]

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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

Re: Machine M, N, O working simultaneously Machine M can produce [#permalink]

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20 Sep 2013, 09:07

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Machine M, N, O working simultaneously Machine M can produce [#permalink]

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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

Re: Machine M, N, O working simultaneously Machine M can produce [#permalink]

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07 Apr 2015, 08:44

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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