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M, N and O can complete the work in 18, 36 and 54 days respectively. M started the work and worked for 8 days, then N and O joined him and they all worked together for some days. M left the job one day before completion of work. For how many days they all worked together?

Correct Answer: 5

Explanation:

Let M, N and O worked together for x days.


From the given data,
M alone worked for 8 days
M,N,O worked for x days
N, O worked for 1 day


But given that
M alone can complete the work in 18 days
N alone can complete the work in 36 days
O alone can complete the work in 54 days


The total work can be the LCM of 18, 6, 54 = 108 units


M's 1 day work = 108/18 = 6 units
N's 1 day work = 108/36 = 3 units
O's 1 day work = 108/54 = 2 units


Now, the equation is
8 x 6 + 11x + 5 x 1 = 108
48 + 11x + 5 = 108
11x = 103 - 48
11x = 55
x = 5 days.


Hence, all M,N and O together worked for 5 days.


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