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Machine M can produce x units in 3/4 of the time it takes machine N to

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Senior Manager
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Machine M can produce x units in 3/4 of the time it takes machine N to [#permalink] New post 11 Jan 2009, 17:31
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Machine M can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x 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: OA

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Last edited by Bunuel on 02 Jul 2015, 13:38, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: Machine M can produce x units in 3/4 of the time it takes machine N to [#permalink] New post 11 Jan 2009, 17:50
Let the following be true:
M makes x in time t
Then the following follows:
N makes x in 4t/3
O makes x in 3/2(4t/3) = 2t
M:N:O = 1:4/3:2=3:4:6
So N=4/(3+4+6)=4/13.
vscid wrote:
Machine M can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x 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

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Re: Machine M can produce x units in 3/4 of the time it takes machine N to [#permalink] New post 13 Jan 2009, 08:48
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vscid wrote:
Machine M can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x 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


For combined rates problems, if you can work out what each machine does in the same amount of time, the problem will almost always become easy. Since x is unimportant here, rather than talk about 'producing x units', I'll simply talk about 'completing one job'. Say it takes M t hours to complete one job. Then we know, from the ratios provided:

M completes one job in t hours
N completes one job in 4t/3 hours
O completes one job in 2t hours

We can easily work out what each would do in 4t hours:

M completes 4 jobs in 4t hours
N completes 3 jobs in 4t hours
O completes 2 jobs in 4t hours

So if they work together for the same amount of time, M does 4/9 of the work, N does 3/9 = 1/3 of the work, and O does 2/9 of the work. The answer is 1/3.
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Re: Machine M can produce x units in 3/4 of the time it takes machine N to [#permalink] New post 13 Jan 2009, 11:32
Exactly ! For combined work problems we cannot simply compare ratios as done in the first explanation.
Thanks Ian.

Now I did the following way: (reverse method)
Let O take t hours
Let N take (2/3)*t hours
Let M take 2/3t(3/4) = (1/2)*t hours

Now using the formula: 1/M + 1/N + 1/O = 1/T ( T = combined hours )

we get, (9/2t) = 1/T.
t = 9T/2 => N = (2/3)*t = (2/3)*(9T/2)

Hence, N = 3 T .
Now, the question is to find fraction of total output T that is produced by N,
so do we have to find T/N ?? or N/T ? :)
Also please let me know if the above approach is wrong.
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Re: Machine M can produce x units in 3/4 of the time it takes machine N to [#permalink] New post 02 Jul 2015, 14:04
We will take all rates in terms of N machine.

Suppose N Machine takes ’n’ Hours
Therefore M machine takes 3/4n hours and O machine takes 3/2 n Hours (n=3/2O)

All machines together in 1 hour will do= 4x/3n+x/n+2x/3n= 3x/n

So all three machines works at the rate of 3x/n and machine N works at the rate of x/n.

Output produced by machine N/Total output= x/n/3x/n= 1/3
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Re: Machine M can produce x units in 3/4 of the time it takes machine N to [#permalink] New post 03 Jul 2015, 00:18
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vscid wrote:
Machine M can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x 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


We can avoid the entire cumbersome calculation of fraction by choosing a RIGHT NUMBER for time and x

Let, x = 24 Units
Let, Time taken by Machine O to produce x(=24) units = 12 mins


i.e. Time taken by Machine O to produce x(=24) units = 12 mins
i.e. Time taken by Machine N to produce x(=24) units = (2/3)*12 = 8 mins
i.e. Time taken by Machine M to produce x(=24) units = (3/4)*8 = 6 mins

Machine O produces 24 units in 12 mins

i.e In 1 min time, the No. of Units produced by Machine O = 24/12 = 2 Units
i.e In 1 min time, the No. of Units produced by Machine N = 24/8 = 3 Units
i.e In 1 min time, the No. of Units produced by Machine M = 24/6 = 4 Units

i.e. Total Units Products by all three machine (M, N and O) together) = 2+3+4 = 9 units

Fraction of Total Work Done by Machine N (in 1 Min) = Units Produced by N / Total Units produced = 3/9 = 1/3

Answer: Option B
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Re: Machine M can produce x units in 3/4 of the time it takes machine N to   [#permalink] 03 Jul 2015, 00:18
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