84 men can complete a work in 30 days. After 15 days, more men were engaged, and the work was completed in 5 days ahead of schedule. How many more people were engaged in total?
42 men
Total work is \(84 \times 30 = 2520\) man-days.
In the first 15 days, work done by 84 men is \(84 \times 15 = 1260\) man-days, so the remaining work is \(2520 - 1260 = 1260\) man-days.
Since the work finishes 5 days early, the total time taken is \(30 - 5 = 25\) days, so the remaining work is completed in \(25 - 15 = 10\) days.
Men required for the remaining work: \(\frac{1260}{10} = 126\). The additional men engaged are \(126 - 84 = 42\).
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