Man-Days and Workforce Problems with Work Rate Examples
Man-Days and Workforce Problems use the relationship between workforce, time and total work. For workers with equal efficiency, total work is measured as men multiplied by days. The same method extends to different working hours, worker efficiencies, men-women ratios, workers joining or leaving, and changing workforce conditions.
On this page
What Are Man-Days and Workforce Problems?
If M workers complete a task in D days, the total work is M × D man-days. For the same work, M₁D₁ = M₂D₂, so increasing the number of workers decreases the required days in inverse proportion. When daily working hours or efficiencies differ, compare total effective work using workers × days × hours × efficiency.
Man-Days and Workforce Problems Video Lessons
Watch short topic-wise lessons for quick revision.
Man-Days Concept in Time and Work
Understand how man-days measure total work and how required time changes when the number of workers increases or decreases.
Man-Days and Workforce Problems Formula & Tricks
Important Formulas
M is the number of equally efficient workers and D is the number of working days.
For the same work and equal worker efficiency and working hours, the product of workers and days remains constant.
For equal worker efficiency, M is workers, D is days and H is working hours per day.
E represents the efficiency factor of each workforce or worker group. Use the same reference unit for all efficiency values.
This formula finds the fraction of a task completed when workforce, days, hours or efficiency changes.
Quick Tricks
If working hours and worker efficiency remain unchanged, workers and days are inversely proportional. Multiply the known workers and days, then divide by the new workforce.
When men, women or children have different efficiencies, express each type in terms of one common worker before applying the man-days formula.
Calculate the effective work done during each period separately, then add the completed work. Do not multiply the total duration by the final workforce.
Man-Days and Workforce Problems Concepts
Basic Man-Days Calculation
If M workers work for D days, the task requires M × D man-days. If the total work is fixed at W man-days, the required days are W ÷ M and the required workers are W ÷ D.
Workforce and Working-Hour Changes
For the same task, M₁D₁H₁ = M₂D₂H₂ if all workers have equal efficiency. A reduction in daily hours must be compensated by more workers or more days.
Different Worker Efficiencies
If one woman is 3/4 as efficient as one man, 4 women produce the work of 3 men. Thus, a group containing M men and W women has equivalent men = M + 3W/4, when the stated efficiency ratio applies.
Workers Joining or Leaving
For equal-efficiency workers and equal daily hours, work completed in an interval is workers × days. If a task requires W man-days, subtract the work already completed to find the remaining man-days, then divide by the current workforce.
Man-Days and Workforce Problems Data Table
Use the structured data below while following the explanation and examples.
Common Workforce Conversions
Equivalent workforce values for common efficiency statements.
| Efficiency statement | Equivalent value | Calculation |
|---|---|---|
| 2 women = 3 men | 1 woman = 1.5 men | 3 ÷ 2 |
| 3 women = 2 men | 1 woman = 2/3 man | 2 ÷ 3 |
| 4 children = 3 men | 1 child = 3/4 man | 3 ÷ 4 |
| 1 man = 2 women | 1 woman = 1/2 man | 1 ÷ 2 |
Note: Use a conversion only when the problem gives or implies the stated efficiency relationship.
Learn more concepts on PrepShots
Start ₹1 Trial →Practice Man-Days and Workforce Problems Questions
Practise published questions related to this topic.
Want more practice questions?
Practice in App →Man-Days and Workforce Problems Quick Quiz
Attempt 5 questions and check your score instantly.
Keep practising
Practice more Man-Days and Workforce Problems questions in the PrepShots app and continue from your current topic.
Practice More Questions - Start ₹1 Trial →Quick Revision Notes
Man-Days and Workforce Problems: Revision Points
Use these formulas and rules to solve workforce-based time and work questions.
- For equal workers and equal hours, man-days = workers × days.
- For the same work, workers × days remains constant when hours and efficiency do not change.
- Include daily hours by using workers × days × hours.
- Include different efficiencies by using workers × days × hours × efficiency.
- Convert women, children or other worker types into equivalent workers before combining them.
- For workers joining or leaving, calculate each interval separately and add the effective man-days.
- Keep all time units consistent: convert hours, days and shifts before applying a formula.
Man-Days and Workforce Problems FAQs
What is the formula for man-days and workforce problems?
For equally efficient workers, total man-days = number of workers × number of days. For the same work, M₁D₁ = M₂D₂.
How many days will 18 workers take to complete 360 man-days of work?
Days = 360 ÷ 18 = 20 days.
What happens to the completion time if the workforce is doubled?
For the same work, unchanged hours and equal efficiency, completion time becomes half because workers and days are inversely proportional.
How do you include working hours in a man-days problem?
Use M₁D₁H₁ = M₂D₂H₂ for equal efficiency. For example, 10 workers working 8 hours are equivalent to 16 workers working 5 hours for the same number of days.
How are men and women combined in workforce questions?
Convert them to one common unit using the given efficiency ratio. If 2 women equal 3 men, then 10 women equal 15 men.
How do you solve a problem where workers join after some days?
Find the work completed before and after the change separately. For example, 8 workers for 5 days and 12 workers for 4 days produce 8 × 5 + 12 × 4 = 88 man-days.