Time and Work Men and Women

CMAT 2024 · Quantitative Techniques & Data Interpretation · Medium · Arithmetic

3 men and 18 women together take 2 days to complete a piece of work. How many days will 9 women alone take to complete the piece of work; if 6 men alone can complete the piece of work in 3 days?

  1. A.

    5

  2. B.

    6

  3. C.

    7

  4. D.

    9

Answer

B

Explanation

Work done by 6 men in 3 days =18m= 18m. Work done by (3m+18w)(3m + 18w) in 2 days =6m+36w= 6m + 36w. Since total work is equal:

18m=6m+36w  ⟹  12m=36w  ⟹  m=3w18m = 6m + 36w \implies 12m = 36w \implies m = 3w

Total work =18(3w)=54w= 18(3w) = 54w. Time taken by 9 women =54w9w=6= \frac{54w}{9w} = 6 days.

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