This problem involves calculating the time required to complete the remaining work after changes in the number of workers and working hours.
Calculate Total Work Required
The total amount of work can be measured in 'man-hours'. Initially, the plan was:
- Number of men: 15
- Number of days: 24
- Hours per day: 8
Total work = Number of men $\times$ Number of days $\times$ Hours per day
Total work = $15 \times 24 \times 8 = 2880$ man-hours.
Calculate Work Done in Initial Phase
The work was carried out for 6 days with the initial setup:
- Number of men: 15
- Number of days worked: 6
- Hours per day: 8
Work done = $15 \times 6 \times 8 = 720$ man-hours.
Calculate Remaining Work
Subtract the work already done from the total work required:
Remaining work = Total work - Work done
Remaining work = $2880 - 720 = 2160$ man-hours.
Calculate New Work Rate and Time Needed
After 6 days, the conditions changed:
- New number of men = 15 + 5 = 20
- New hours per day = 6
Let the number of additional days required be $D$. The remaining work must be completed by the new workforce under the new conditions.
Remaining work = New number of men $\times$ Additional days ($D$) $\times$ New hours per day
$2160 = 20 \times D \times 6$
$2160 = 120 \times D$
$D = \frac{2160}{120}$
$D = 18$ days.
Therefore, 18 more days will be required to finish the remaining work.
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