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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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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?

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

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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?

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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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.

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

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

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15 Jul 2016, 02:33

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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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17 Jul 2016, 06:40

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, 02:53, edited 1 time in total.

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

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03 Feb 2017, 20:32

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.

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

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05 Feb 2017, 05:20

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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