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Three men and eight machines can finish a job | Quantitative Aptitude – Arithmetic – Time and Work

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The question below is from previous year CAT question from CAT 2019 exam comes from Arithmetic – Time and Work: Three men and eight machines can finish a job. Find out by answering this question which tests an aspirant’s Quantitative Ability Skills:

CAT 2019 – Slot -1 - Question 5 - Three men and eight machines can finish a job

Q. 5: 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 a man can finish the job alone in M days.

Given two machines can finish the job in 13 days so one machine can finish the job in 13*2 = 26 days

As given that 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

So 3/M + 8/26 = 2(8/M + 3/26)

3/M + 4/13 = 16/M + 3/26

16/M – 3/M = 4/13 – 3/13

13/M = 1/13

M = 169

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