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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Important Questions from Time and Work
A and B can do a piece of work in 18 days. B and C together can do it in 30 days. If A is twice as good a workman as C, find in how many days B alone can do the work?
Two men and 7 women can complete a work in 28 days, whereas 6 men and 16 women can do the same work in 11 days. In how many days will 5 men and 4 women, working together, complete the same work?
A man and a woman, working together can do a work in 66 days. The ratio of their working efficiencies is 3 ∶ 2. In how many days 6 men and 2 women together can do the same work?
Each one of five men independently can complete a work in 20 days. The work is started by one person. Next day one more person joins and every next day one more person joins. From the fifth day, five persons continued working as a team. In how many days, will the work be completed?
Numan does half the work as Gagan in 4/5 of the time. If together they take 16 days to complete a piece of work, then how long will it take Gagan to complete the work?
