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

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New post 11 Jan 2009, 18:31
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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, 14:38, 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]

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New post 11 Jan 2009, 18:50
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]

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New post 13 Jan 2009, 09:48
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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]

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New post 13 Jan 2009, 12:32
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]

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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]

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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]

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

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New post 17 Jul 2016, 07:40
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


Another way to look at the problem..

Time ratio for M and N

M:N = 3:4....Efficiency(or work done in the same time) Ratio will be the inverse of this..m:n = 4:3

Similarly..Eff. Ratio for N and O
n:o = 3:2

Overall
m:n:o = 4:3:2

Fraction of work done by N?

\(\frac{3}{4+3+2}\)

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

(B)

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Last edited by ShashankDave on 18 Jul 2016, 03:53, edited 1 time in total.

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

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New post 17 Jul 2016, 19:07
let m,n,o times=3/2,2,3
m,n,o rates=2/3,1/2,1/3
combined rate=3/2
(1/2)/(3/2)=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]

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New post 03 Feb 2017, 08:02
Machine O: time y; rate o; y*o=x; o=x/y
Machine N: time 2/3y; rate n; 2/3y*n=x; n=3x/2y
Machine M: time 3/4*2/3*y=y/2; rate m; y/2*m=x; m=2x/y

Total rate: x/y+3x/2y+2x/y=9x/2y
Rate of n/Total rate=3x/2y / 9x/2y= 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]

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New post 03 Feb 2017, 21:32
I simply plugged in numbers for this question.
Let's say X= 100

M= 45 mins to produce 100 units
N= 60 mins to produce 100 units
O= 90 mins to produce 100 units

Combined (1/45) + (1/60) + (1/90) = 9/180, which we flip to give us 20 mins that it will take for the 3 machines combined to produce 100 units. From here we just use 20/N total time so 20/60 to get 1/3 which is choice B.

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Re: Machine M can produce x units in 3/4 of the time it takes machine N to [#permalink]

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New post 04 Feb 2017, 09:07
Let, M takes 3 hours
So, N takes 4 hours
And O takes 6 hours

LCM of 3, 4, and 6 is 12
In 12 hours M produces 4x
In 12 hours N produces 3x
In 12 hours O produces 2x

In 12 hours, total production by M, N, and O is 9x out of which N produces 3x, i.e., 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]

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New post 05 Feb 2017, 06:20
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


Let the time taken be as under -

O = 12
N = 8
M = 6

Assume total Work be 24 units...

Thus efficiency of the 3 machines are as under -

O = 2
N = 3
M = 4

Total efficiency is 9 ( ie, 2 + 3 + 4 ) units/hr

So, work done by N is 3/9 = 1/3

Hence, answer will be (B) 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] 05 Feb 2017, 06:20
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