# Contractor took a job to be done in 20 days. But 12 men did not come up and was finished by remaining man in 32 days.

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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?

posted Nov 17, 2016

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.

20x=(x-12)*32
X=32

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