Work and Time Calculation
This problem involves an inverse relationship between the number of workers and the time taken to complete a job. If the time decreases, the number of workers must increase proportionally.
Calculating Total Work
The total amount of work required to build the wall is constant. We can calculate it by multiplying the initial number of workers by the time they took.
Total Work = (Number of Workers) \times (Number of Days)
Total Work = 15 \text{ workers} \times 10 \text{ days} = 150 \text{ worker-days}
Determining Workers Needed
Now, we need to find out how many workers are needed to complete the same 150 worker-days of work in just 6 days.
Let the required number of workers be 'W'.
W \times 6 \text{ days} = 150 \text{ worker-days}
To find W, we rearrange the equation:
W = \frac{150 \text{ worker-days}}{6 \text{ days}}
W = 25 \text{ workers}
Conclusion
Therefore, 25 workers are needed to build the wall in 6 days.
Important Questions from Time & Work (Notes)
- A fresh water tap fills a fish tank in 40 minutes. The same tank is filled by a salt water tap in 120 minutes. If both the taps are open, how many minutes will it take to fill the tank?
- A completes $\frac{7}{10}$ of a work in 15 days and then he completes the remaining work with the help of B in 5 days. In how many days can A and B together complete the entire work?
Aman can do 50% of the job in 16 days, and Bhanu can do 25% of the job in 24 days. In how many days can they do $\frac{1}{4}^{th}$ of the job working together ?
- X can finish a job in $141$ days. He worked for $57$ days alone and the remaining work was completed by Y, in $84$ days. How many days would both together take to complete the entire job?
Ravina, Sujata, and Saroj can complete a work of painting separately in 32, 48, and 64 hours, respectively. They started working together, but Saroj left after 5 hours. From the 6th hour, Ravina and Sujata decided to work on alternate hours starting with Ravina. In how much time will the entire work of painting be completed?
