How Many Extra Men Are Needed to Finish Work on Time? - A Step-by-Step Guide

Step-by-Step Guide to Determine Extra Manpower Required

Project management often requires careful calculation to ensure work is completed on time. This article provides a detailed guide on how to determine the number of extra men needed to finish a task within a specified timeframe. We consider three scenarios and use an analytical approach to solve them efficiently. This technique can be applied to real-world projects to calculate the necessary manpower.

Problem 1: 150 Men in 100 Days with 75% Completion

Let W denotes the whole given work, and N denotes the number of additional men required. We start by understanding the rate of work done per man per day. Assuming all men have equal work efficiencies, we have:

W/150/100 1

- 75/100W/150 N/100 80

[ constant rate of work done per man per day]

Rewriting this equation:

150N 5/4150
N 150/4 37.5 ≈ 38

Answer: 38 extra men are required.

Problem 2: 16 Men in 20 Days with 50% Completion

To calculate the number of additional men needed, we need to find the remaining work and the time left. We can use the following steps:

W/2/16/12 W - W/2/16N/20 - 12

[ constant rate of work done per man per day]

Rewriting this equation:

816N 1612
16N 24
N 8

Answer: 8 additional men are required.

Problem 3: Initial 20 Men in 30 Days with 25% Completion

Let's solve the challenge of needing to complete 75% of a task within 30 days after 15 days of work has been done. The sequence of solving this problem is as follows:

1. Total Work in Man-Days

Total work 20 men times; 30 days 600 man-days

2. Work Done in 15 Days

Work completed in 15 days 20 men times; 15 days 300 man-days
However, only 25% of the work is finished.
Work done 0.25 times; 600 150 man-days

Remaining work 600 - 150 450 man-days

3. Time Left

Total time 30 days
Time spent 15 days
Remaining time 30 - 15 15 days

4. Extra Men Required

Lets x be the number of men required to complete the remaining work in 15 days.
The equation for the remaining work is: x men times; 15 days 450 man-days
Solving for x:
x 450 man-days / 15 days 30 men

Initial men 20
Extra men required 30 - 20 10 men

Conclusion: 10 extra men are required to finish the work on time.

Conclusion

In project management, accurately determining the required manpower is crucial for timely completion. The techniques used here demonstrate the importance of understanding work rates, man-days, and remaining work to make informed decisions. These methods can be applied to various scenarios to ensure optimal allocation of resources and avoid delays.