A contractor took a job for his group to do in 20 days. But 12 men did not come up for the job and job was done by remaining man in 32 days. What was the original size of the contractor’s team?

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A contractor took a job for his group to do in 20 days. But 12 men did not come up for the job and job was done by remaining man in 32 days. What was the original size of the contractor’s team?

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If the initial workforce = N. It's given that N people completed 1 job in 20 days and (N-12) people completed the same job in 32 days.

Work speed of N people = (1 job / 20 days)=(1/20)

Work speed of a person = (1 job / (20 days*N))=(1/(20*N))

Work speed of 12 people = (1 job / 20 days)*(12/N) =12/(20*N)

Work speed of (N-12) people = (1/20)-(12/(20*N)) = 1/32

Rearranging for N gives N = 32.

That means the initial workforce consisted of 32 people.

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