Efficiency of Men and Boys in Work Allocation

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 boys

Step 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.

Related Keywords

man-days boy-days work allocation