Multiple choice

4 men and 6 women complete a task in 24 days. If the women are at least half as efficient as the men, but not more efficient than the men, what is the range of the number of days for 6 women and 2 men to complete the same task?

  1. 25 to 28 days

  2. 28.1 to 29.9 days

  3. 30 to 33.6 days

  4. 33.7 to 39.9 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let M and W be the efficiency of a man and a woman. 4M + 6W = 1/24. Given 0.5M <= W <= M. For 6W + 2M, we calculate the time T = 1 / (6W + 2M). Substituting the bounds for W, we find the range of T.

AI explanation

The total work is 4 men and 6 women working for 24 days, or 96 man-days plus 144 woman-days. Assuming a woman is half as efficient as a man (1 woman = 0.5 man), the total work is 96 + 72 = 168 man-days. For 6 women and 2 men (equivalent to 5 men), the time taken is 168 divided by 5, or 33.6 days. At the other extreme, assuming a woman is as efficient as a man, the total work is 96 + 144 = 240 man-days, and the team of 8 effective men takes 240 divided by 8, or 30 days. This gives a range of 30 to 33.6 days.

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