m6 ques 21

Question

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?

* 14
 * 13
 * 11
 * 9
 * 7

In this question, shouldn't Machine A's no. of days to do the job working 1.5 shifts be 18?
Because working 2 shifts, its 12 and working 1 shift its 24.
Please tell me what am I missing here .

mads · Answer

This is my approach.
A can do the job in 12 days working two shifts => Number of shifts A takes to complete the job is = 2*12 = 24 shifts.
Work done by A per shift = 1/24

B can do the job in 15 days working two shifts =>Number of shifts B takes to complete the job is = 2*15 = 30 shifts.
Work done by B per shift = 1/30

Machine A is utilized during the first shift and Machine B during the second shift, while both work half of the third shift => Per day there are three shifts.

First shift A is utilized => work done = 1/24
Second shift B is utilized => work done = 1/30
Work done by A in half shift + Work done by B in half shift = 1/(2*24) + 1/(2*30) = 1/48+1/60.

Total work done in a day (shift1+shift2+shift3) = 1/24+1/30+(1/48+1/60)
Solving this gives us 9/80 as the work done per day.
So number of days required to complete the job = 80/9 which is nearly equal to 9 days.

My Answer is D.

Please post the OA.

m6 ques 21

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