One contractor had undertaken a construction work. To complete the given job, he sought labour comprising 24 men for 12 days for working 10 hours a day. But due to festival season, as the labour had gone to their respective hometowns, he could get only 15 men and they too were willing to work 8 hours a day. With this much labour, in how many days would he be able to complete the same job?
Work Calculation: Job Completion Time
This problem involves calculating the time required to complete a job when the number of workers and their daily working hours change. The fundamental principle is that the total amount of work needed for the job remains constant.
The total work can be represented as the product of the number of workers, the number of days they work, and the hours they work each day:
$Total Work = (Number of Men) × (Number of Days) × (Hours per Day)$
Initial Plan Work Units
The contractor's original plan was:
- Number of Men: 24
- Number of Days: 12
- Hours per Day: 10
Calculate the total work units (in man-hours) required for the job based on this plan:
$Total Work = 24 men × 12 days × 10 hours/day = 2880 man-hours$
Revised Plan Setup
Due to circumstances, the available workforce and working hours changed:
- Number of Men: 15
- Hours per Day: 8
- Number of Days: $D$ (This is what we need to find)
The total work required (2880 man-hours) remains the same.
Days Required Calculation
Set up the equation for the revised plan using the known total work:
$2880 man-hours = 15 men × D days × 8 hours/day$
Simplify the equation:
$2880 = 120 × D$
Now, solve for $D$ by dividing the total work by the combined daily output of the revised workforce:
$D = &frac{2880}{120}$
$D = 24$
Job Completion Result
Therefore, with 15 men working 8 hours a day, the contractor will complete the same construction job in 24 days.
Important Questions from Work Efficiency
- M is thrice as efficient as workman as N and therefore is able to finish a job in 264 days less than N. Then in how many days can N finish the entire work?
- A can do a piece of work in $1455$ days. B is $25\%$ more efficient than A. Find the number of days taken by B to do the same piece of work.
- 45 people take 18 days to dig a pond. If the pond would have to be dug in 15 days, then the number of people to be employed will be
- A stock of food is enough for 240 men for 48 days. How long will the same stock last for 160 men?
Rajender engages Sunil and Vijay to do some construction work in his office. Sunil is highly skilled and is $3\frac{1}{2}$ times as good a workman as Vijay. Therefore, he is able to finish his work in 45 days less than Vijay. In how many days they both working together, can finish the work?
