Multiple choice

81 men can construct a 200-m long wall in 24 days, working 6 hours a day. If 27 men leave the work after 6 days, then how many hours per day should the remaining men work to complete the work in the remaining days?

  1. 9

  2. 16

  3. 32

  4. 48

  5. 4
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A Correct answer
Explanation

Work = Men * Days * Hours. Total work = 81 * 24 * 6 = 11664 man-hours. Work done in 6 days = 81 * 6 * 6 = 2916. Remaining work = 11664 - 2916 = 8748. Remaining men = 81 - 27 = 54. Remaining days = 24 - 6 = 18. Hours needed = 8748 / (54 * 18) = 8748 / 972 = 9.

AI explanation

Using the man-hours formula, the total work is 81 men times 24 days times 6 hours per day, which equals 11664 man-hours. In the first 6 days, the 81 men complete 81 times 6 times 6, or 2916 man-hours, leaving 8748 man-hours of work. The remaining time is 18 days and the remaining workforce is 54 men (81 minus 27), so dividing 8748 man-hours by 54 men and 18 days gives 9 hours per day.

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