Multiple choice

If 12 men or 20 women can do a piece of work in 54 days, then in how many days can 9 men and 12 women together do the work?

  1. 28 days

  2. 3 days

  3. 21 days

  4. 40 days

  5. 48 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

12 men = 20 women, so 1 man = 5/3 women. 9 men + 12 women = 9(5/3) + 12 = 15 + 12 = 27 women. 20 women take 54 days. 27 women take (20 * 54) / 27 = 20 * 2 = 40 days.

AI explanation

Given the equivalence of 12 men to 20 women, the work capacity ratio of a man to a woman is 20 to 12, or 5 to 3. Let the total work be the Least Common Multiple of the given worker counts and days, which is 1080 units; a man does 2 units per day and a woman does 1.2 units. The combined daily output of 9 men and 12 women is (18 + 14.4) = 32.4 units. Dividing the total work of 1080 units by 32.4 gives 40 days.

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