machine work!

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machine work!

by vscid » Tue Apr 06, 2010 6:28 pm
A furniture manufacturer has two machines, but only one can be used at a time. Machine A is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine A can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule?


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by 4GMAT_Mumbai » Tue Apr 06, 2010 6:55 pm
IMO, the answer is 9 days.

The good part is that we do not have to do full calculations. We can figure out that the work gets done on the 9th day (without having to figure out as to how many hours into the day or as to how many shifts into the day)

A finishes the job in 24 shifts. B finishes in 30 shifts.

Part of the job done per day = (1/24 + 1/30 + 1/48 + 1/60).

Small suggestion - Do not take LCM of 24, 30, 48 and 60. Just add 1/24 and 1/48 first. Add 1/30 and 1/60 next. You are left with 1 / 16 + 1 / 20 = 9 / 80.

At the end of the 8th day, 72 / 80 parts of the job are done. At the end of the 9th day, 81 / 80 parts of the job are done - implying that the work gets done a few hours before the day ends. But, it does not matter as far as the question is concerned.

Hope this helps.

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by eaakbari » Tue Apr 06, 2010 8:35 pm
While doing 2 shifts A takes 12 days to complete,
therefore while doing 1 shift hell take 24
or doing 1.5 shifts(amount done in one day) he takes 16

Similarly B working everyday 1.5 shifts will take 20 days.

Now

1/20 + 1/16 = 1/x

x = 8.88 = 9 days