Multiple choice

A contract is to be completed in 56 days and 104 men are set to work, each working 8 hours a day. After 30 days, 2/5 of the work is finished. How many additional men may be employed so that the work may be completed on time, if each man is working 9 hours per day now?

  1. 56

  2. 65

  3. 46

  4. None of the above
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A Correct answer
Explanation

Work done = 104 * 30 * 8 = 24960 man-hours. This is 2/5 of total work, so total work = 62400 man-hours. Remaining work = 37440 man-hours. Time remaining = 56 - 30 = 26 days. Men needed = 37440 / (26 * 9) = 160. Additional men = 160 - 104 = 56.

AI explanation

Using the work formula (M1 * D1 * H1) / W1 = (M2 * D2 * H2) / W2, we have 104 men working 30 days at 8 hours to finish 2/5 of the work. For the remaining 3/5 of the work to be finished in 26 days at 9 hours per day, the equation becomes (104 * 30 * 8) / (2/5) = (M * 26 * 9) / (3/5). Solving this gives M = 160, so the total men now required is 160. Since there were already 104 men, the number of additional men to employ is 160 - 104 = 56.

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