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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

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

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

But given thatM alone can complete the work in 18 daysN alone can complete the work in 36 daysO 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 unitsN's 1 day work = 108/36 = 3 unitsO's 1 day work = 108/54 = 2 units

Now, the equation is8 x 6 + 11x + 5 x 1 = 10848 + 11x + 5 = 10811x = 103 - 4811x = 55x = 5 days.

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

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