Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job. If two machines can finish the job in 13 days, then how many men can finish the job in 13 days?
Explanation:
Let the work done by one man and one machine per day be x and y respectively.
Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job.
Since efficiency is inversely proportional to the time taken, so the efficiency of 3 men and 8 machines is twice that of 8 men and 3 machines.
∴ (3x + 8y) = 2(8x + 3y)
∴ 13x = 2y.
So, work done by 13 men in a day = work done by 2 machines in a day.
∴ If two machines can finish the job in 13 days, same work will be done by 13 men in 13 days.
Hence, 13.
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