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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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Updated on: 02 Jul 2015, 14:38
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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
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Originally posted by vscid on 11 Jan 2009, 18:31.
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
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03 Jul 2015, 01:18
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 minsi.e. Time taken by Machine O to produce x(=24) units = 12 minsi.e. Time taken by Machine N to produce x(=24) units = (2/3)*12 = 8 minsi.e. Time taken by Machine M to produce x(=24) units = (3/4)*8 = 6 minsMachine O produces 24 units in 12 minsi.e In 1 min time, the No. of Units produced by Machine O = 24/12 = 2 Unitsi.e In 1 min time, the No. of Units produced by Machine N = 24/8 = 3 Unitsi.e In 1 min time, the No. of Units produced by Machine M = 24/6 = 4 Unitsi.e. Total Units Products by all three machine (M, N and O) together) = 2+ 3+ 4 = 9 unitsFraction 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
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13 Jan 2009, 09:48
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
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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
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02 Jul 2015, 15:04
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 Thanks
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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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Updated on: 18 Jul 2016, 03:53
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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Originally posted by ShashankDave on 17 Jul 2016, 07:40.
Last edited by ShashankDave on 18 Jul 2016, 03:53, edited 1 time in total.



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Re: Machine M can produce x units in 3/4 of the time it takes machine N to
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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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Machine Mean produce x units in 3/4 of the time it takes machine N to
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18 Feb 2018, 23:09
Bunuel 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 If Machine N takes 120 minutes to produce x units, machine M will take \(\frac{3}{4}*120 = 90\) minutes. Similarly, as Machine N will take \(\frac{2}{3}\)rd of the time to produce the units machine O produces. \(120 = \frac{2}{3}*x\) > \(x = 120*\frac{3}{2} = 180\) minutes If 360 units are being produced, machine N will produce 3 units in a minute, machine M will produce 4 units in a minute, and machine O will produce 2 units in a minute. Therefore, machine N will produce \(\frac{3}{3+4+2} = \frac{3}{9} = \frac{1}{3}\) of the total units (Option B)
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Re: Machine Mean produce x units in 3/4 of the time it takes machine N to
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24 Mar 2018, 07:35
Bunuel 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 Attachment:
MACHINES M, N AND O.PNG [ 2.28 KiB  Viewed 890 times ]
Let the total work be 24 units so, efficiency of the machines are Attachment:
MNO Efficiency.PNG [ 2.91 KiB  Viewed 892 times ]
Since all the 3 machines are working simultaneously work done by N is \(\frac{3}{(2+3+4)}\) = \(\frac{1}{3}\) , Answer must be (B)
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Re: Machine Mean produce x units in 3/4 of the time it takes machine N to
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05 Apr 2018, 11:10
Bunuel 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 t = the time it takes machine O to produce x units; then the time it takes machine N to produce x units = (2/3)t, and the time it takes machine M to produce x units = (3/4)(2/3)t = (1/2)t. Therefore, the rate of M is x/[(1/2)t] = 2x/t, the rate of N is x/[(2/3)t] = 3x/2t, and the rate of O is x/t. Their combined rate is 2x/t + 3x/2t + x/t = 4x/2t + 3x/2t + 2x/2t = 9x/2t. If all three machines are working simultaneously, the fraction of the total output that is produced by machine N is: (3x/2t)/(9x/2t) = 3x/9x = 1/3 Alternate Solution: Let’s denote the number of units produced by machine O in 12 hours as y. Since machine N can produce the same number of units in 2/3 of the time, machine N can produce y units in 8 hours. Since machine M can produce the same number of units in 3/4 of the time necessary for machine N, machine M can produce y units in 6 hours. Now, let’s suppose all the machines ran for 24 hours. In 24 hours, machine M will produce 4y units; machine N will produce 3y units, and machine O will produce 2y units. The total number of units produced is 4y + 3y + 2y = 9y. The number of units produced by machine N is 3y, which is (3y)/(9y) = 1/3 of all the units produced. Answer: B
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