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)
- If 6 men and 8 boys can do a piece of work in 10 days and 26 men and 48 boys can do the same work in 2 days, then the time taken by 15 men and 20 boys to do the same work will be
- 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?
Three pipes A, B and C can fill a tank in $10$, $15$ and $20$ hours respectively. Pipe A was opened at $6$ AM, pipe B at $7$ AM and pipe C at $8$ AM. At what time was the tank completely filled, if pipe C needs a break of $1$ hour after remaining open for $3$ hours?
A tank has four pipes $P_1$, $P_2$, $P_3$ and $P_4$. The tank can be filled in $15$ minutes by pipes $P_1$, $P_2$, $P_3$ together. It can be filled in $20$ minutes by pipes $P_2$, $P_3$, $P_4$ together and it can be filled by pipes $P_1$, $P_4$ together in $30$ minutes. If all the pipes are opened together, then in how much time will the tank be filled?
$5$ men and $4$ women can earn ₹ $20000$ in $8$ days. $10$ men and $7$ women can earn ₹ $23,750$ in $5$ days. In how many days will $5$ men and $6$ women earn ₹ $12,000$?
