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CAT 2019 Quant Question with Solution 15

Question:
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?

Let one machine completes 1 unit of work per day.

Given, two machines can finish the job in 13 days

Therefore, the work of 2×1×13 = 26 units.

Also, let on man completes m units of work per day.

From the given condition:

3m+8×1 = 2(8m+3×1)

Or m = $\frac{2}{13}units$

Let it require ‘x’ number of men to complete the work in 13 days.

Therefore, xm×13 =26 units

Or x = 13 men

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