Answer :
Sure! Let's break this down step-by-step.
### Step 1: Determine the total work in "man-days"
First, we need to understand the amount of work involved with the initial condition. Given that 4 men can complete the work in 5 days, we compute this as follows:
[tex]\[ \text{Total Work} = 4 \text{ men} \times 5 \text{ days} = 20 \text{ man-days} \][/tex]
### Step 2: Calculate the total work required for the new task
Next, we know that the new task is twice the magnitude of the original work. Thus, we need:
[tex]\[ \text{Total Work Required} = 2 \times 20 \text{ man-days} = 40 \text{ man-days} \][/tex]
### Step 3: Determine the number of days required for 10 men to complete the new task
Now we need to find out how many days it will take for 10 men to complete the 40 man-days of work. This can be calculated by dividing the total man-days of work by the number of men:
[tex]\[ \text{Number of days} = \frac{40 \text{ man-days}}{10 \text{ men}} = 4 \text{ days} \][/tex]
### Conclusion
It will take 10 men 4 days to complete a work that is twice the magnitude of the initial work that 4 men can complete in 5 days.
### Step 1: Determine the total work in "man-days"
First, we need to understand the amount of work involved with the initial condition. Given that 4 men can complete the work in 5 days, we compute this as follows:
[tex]\[ \text{Total Work} = 4 \text{ men} \times 5 \text{ days} = 20 \text{ man-days} \][/tex]
### Step 2: Calculate the total work required for the new task
Next, we know that the new task is twice the magnitude of the original work. Thus, we need:
[tex]\[ \text{Total Work Required} = 2 \times 20 \text{ man-days} = 40 \text{ man-days} \][/tex]
### Step 3: Determine the number of days required for 10 men to complete the new task
Now we need to find out how many days it will take for 10 men to complete the 40 man-days of work. This can be calculated by dividing the total man-days of work by the number of men:
[tex]\[ \text{Number of days} = \frac{40 \text{ man-days}}{10 \text{ men}} = 4 \text{ days} \][/tex]
### Conclusion
It will take 10 men 4 days to complete a work that is twice the magnitude of the initial work that 4 men can complete in 5 days.
