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Machine M can produce x units in 3/4 of the time it takes...

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by BTGmoderatorLU » Mon Mar 05, 2018 1:43 pm
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

The OA is B.

I'm confused by this PS question. Experts, any suggestion about how to solve it? Thanks in advance.
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by mbawisdom » Mon Mar 05, 2018 1:51 pm
LUANDATO 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

The OA is B.

I'm confused by this PS question. Experts, any suggestion about how to solve it? Thanks in advance.
Let's start with Machine O since this one is the slowest. We can assign it a rate of R.
Machine N takes 2/3 of the time of Machine O so it has a rate that is 3/2 faster than Machine O--> rate is 1.5R
Machine M takes 3/4 of the time of Machine N so it has a rate that is 4/3 faster than Machine N --> rate is (4/3)(3/2)R = 2R

Together the machines have a rate of R + 1.5R + 2R = 4.5R
Rate of Machine N/Total Rate = 1.5R/4.5R = 1/3

Answer is B.
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by [email protected] » Mon Mar 05, 2018 2:17 pm
Hi LUANDATO,

We're told that Machine M can produce X units in 3/4 of the time it takes machine N to produce X units and Machine N can produce X units in 2/3 the time it takes machine O to produce X units. We're asked if all three machines are working simultaneously, what fraction of the total output is produced by machine N. This question can be solved by TESTing VALUES (but you need to focus on the amount of TIME each Machine takes and NOT the value of X).

IF... Machine O takes 12 hours to produce X units and....
Machine N takes (2/3)(12) = 8 hours to produce X units and....
Machine M takes (3/4)(8) = 6 hours to produce X units....

Let's have the Machines work for 24 hours...
Machine O will make (24/12)(X) = 2X units
Machine N will make (24/8)(X) = 3X units
Machine O will make (24/6)(X) = 4X units

2X + 3X + 4X = 9X total units produced. Machine N produces (3X)/(9X) = 1/3 of the units

Final Answer: B

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by swerve » Tue Mar 06, 2018 7:49 am
Hi LUANDATO,

Another way to look at the problem can be as follow,

Let the time taken be as

M = 12
N = 8
O = 6

Assume total work be 24 units.

Thus the efficiency of the three machines are asunder,

O = 2
N = 3
M = 4

Total efficiency is 9 (i.e 2 + 3 + 4)units/h

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

Regards!
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by Jeff@TargetTestPrep » Thu Mar 08, 2018 4:38 pm
LUANDATO 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

Answer: B

Jeffrey Miller
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