Solving the Work Allocation Problem: How Many Days Will 4 Men and 17 Boys Take?
This article provides a detailed step-by-step solution to a classic work allocation problem. From determining the work rate to finalizing the number of days required, we'll walk through the process of solving such problems in the context of man-days and boy-days. By understanding the principles involved, you can efficiently allocate resources in your projects and problems.
Understanding the Problem
The problem states that 5 men or 10 boys can complete a work in 5 days. The challenge is to determine how many days it will take for 4 men and 17 boys to complete the same work.
Step-by-Step Solution
Step 1: Calculate Work Done
First, let's calculate the total work done in terms of man-days and boy-days.
Total Work in man-days:5 men × 5 days 25 man-days
Total Work in boy-days:10 boys × 5 days 50 boy-days
Step 2: Establishing the Relationship
We can now establish a relationship between these two units of work:
25 man-days 50 boy-days 1 man 2 boysStep 3: Convert Men to Boys
Convert the 4 men into an equivalent number of boys:
4 men 4 × 2 boys 8 boys
Step 4: Total Equivalent Workers
Now, find the total equivalent number of boys when combined with 17 boys:
8 boys 17 boys 25 boys
Step 5: Calculate Time to Complete Work
Given that the total work is 50 boy-days, we can calculate the number of days required for 25 boys to complete the work:
Days required 50 boy-days ÷ 25 boys 2 days
Conclusion
Therefore, 4 men and 17 boys will complete the work in 2 days.
Alternative Solutions and Insights
Let's explore another approach to the same problem:
Approach 1
We know that:
5 men 10 boys (Given)
1 man 2 boys
4 men 17 boys 8 boys 17 boys 25 boys
Total boy-days required to complete 5 × 10 50 boy-days
Since 25 boys can do 50 boy-days in 2 days, they can complete the work in 2 days.
Approach 2
We can express the work rate in terms of boy-days:
Total work 50 boy-days
4 men 17 boys 25 boys
Days required 50 boy-days ÷ 25 boys 2 days
Key Takeaways
Understanding the concept of man-days and boy-days can help you efficiently allocate resources in various problems. By converting and calculating the equivalent units, you can determine the number of days required for a given set of workers to complete a task.