Men and Machine Efficiency Comparison

CAT 2019 Slot 1 · QA · Medium · Work, time

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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?

Answer

13

Explanation

Let efficiency of 1 man be MM and 1 machine be mm. 3M+8m=2(3m+8M)  ⟹  3M+8m=6m+16M  ⟹  2m=13M3M + 8m = 2(3m + 8M) \implies 3M + 8m = 6m + 16M \implies 2m = 13M. Two machines do the work in 13 days   ⟹  Work=2m×13=13M×13\implies \text{Work} = 2m \times 13 = 13M \times 13. Number of men needed to finish in 13 days =13M×13M×13=13= \frac{13M \times 13}{M \times 13} = 13.

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