Multiple choice

A group of 25 men and 15 women can do a piece of work in 12 days. The women leave after 8 days and the remaining work is completed by 25 men in 6 days. How many days will 15 women take to do the same work?

  1. 12 days

  2. 36 days

  3. 24 days

  4. 30 days

  5. 35 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total work = (25m + 15w) * 12. Work done in 8 days = (25m + 15w) * 8. Remaining work = (25m + 15w) * 4. This is done by 25m in 6 days: (25m + 15w) * 4 = 25m * 6. Simplifying, 100m + 60w = 150m, so 60w = 50m, or 6w = 5m. Total work = (25 * (6/5)w + 15w) * 12 = 45w * 12 = 540w. 15 women take 540/15 = 36 days.

AI explanation

Let the total work be 1 unit, with the combined daily work of 25 men and 15 women being 1/12. In 8 days, the group completes 8/12 or 2/3 of the work, leaving 1/3 of the work for the 25 men to finish in 6 days. This means 25 men complete 1/18 of the work per day, so their contribution to the original combined daily rate is 1/18. Subtracting this from the combined rate of 1/12 leaves 1/36, which represents the daily work of the 15 women. Since 15 women complete 1/36 of the work per day, they will finish the entire job in 36 days.

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