Machine M, N, O working simultaneously. Machine M can...

[swerve]

Machine M, N, O working simultaneously. Machine M can produce x units in 3/4 of the it takes machine N to produce the same amount of units. Machine N can produce x units in 2/3 of 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 produce by machine N?

A. 1/2
B. 1/3
C. 4/13
D. 8/29
E. 6/33

The OA is B.

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[GMATGuruNY]

Machine M, N, O working simultaneously. Machine M can produce x units in 3/4 of the it takes machine N to produce the same amount of units. Machine N can produce x units in 2/3 of 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 produce by machine N?

A. 1/2
B. 1/3
C. 4/13
D. 8/29
E. 6/33

Let O's time to produce x units = 12 hours.
Since N's time is 2/3 of O's time, N's time to produce x units = (2/3)(12) = 8 hours.
Since M's time is 3/4 of N's time, M's time to produce x units = (3/4)(8) = 6 hours.

Let x = 24 units.
Since O takes 12 hours to produce 24 units, O's rate = w/t = 24/12 = 2 units per hour.
Since N takes 8 hours to produce 24 units, N's rate = w/t = 24/8 = 3 units per hour.
Since M takes 6 hours to produce 24 units, M's rate = w/t = 24/6 = 4 units per hour.
Combined hourly rate for O, N and M = 2+3+4 = 9 units per hour.
Fraction produced each hour by N = (N's hourly rate)/(combined hourly rate for all 3 machines) = 3/9 = 1/3.

The correct answer is B.

[Jeff@TargetTestPrep]

Machine M, N, O working simultaneously. Machine M can produce x units in 3/4 of the it takes machine N to produce the same amount of units. Machine N can produce x units in 2/3 of 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 produce 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 x.

Since machine N can produce the same number of units in 2/3 of the time, machine N can produce x 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 x units in 6 hours.

Now, let's suppose all the machines ran for 24 hours. In 24 hours, machine M will produce 4x units; machine N will produce 3x units and machine O will produce 2x units. The total number of units produced is 4x + 3x + 2x = 9x. The number of units produced by machine N is 3x, which is (3x)/(9x) = 1/3 of all the units produced.

Answer: B