Men, Women and Children Work Efficiency Explained
Men, women and children work efficiency problems compare the daily work rates of different worker types. Convert the given worker relationship into an efficiency ratio, then use persons, days and efficiency to calculate total work, completion time or the required number of workers.
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What Is Men, Women and Children Work Efficiency?
If one man, one woman and one child have efficiencies m, w and c, respectively, then the work completed by M men, W women and C children in D days is D(Mm + Ww + Cc). For example, if 2 men = 3 women = 6 children in work capacity, then one man : one woman : one child = 3 : 2 : 1.
Men, Women and Children Work Efficiency Video Lessons
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Work Efficiency: Men, Women and Children
Learn how to compare the work efficiencies of men, women and children using efficiency ratios in Time and Work problems.
Men, Women and Children Work Efficiency Formula & Tricks
Important Formulas
Here, m, w and c are the daily efficiencies of one man, one woman and one child.
The ratio is obtained by assigning a common amount of work to the given groups and simplifying their individual rates.
Use the combined daily efficiency of all workers as the divisor.
This converts women and children into the number of men producing the same daily work.
Quick Tricks
When a question states that groups of men, women and children do equal work, assign the same value to each group. Dividing this common value by the number of workers gives their individual efficiency ratio.
Choose one worker type as the base and express every other worker in that unit before calculating time. This avoids adding unlike efficiency values directly.
Men, Women and Children Work Efficiency Concepts
Finding the individual efficiency ratio
Suppose a men group, women group and children group complete equal work: a men = b women = c children. Taking the common group work as abc units gives the individual efficiencies bc, ac and ab. Therefore, one man : one woman : one child = bc : ac : ab.
Calculating combined daily work
Use the efficiency ratio as daily work units. If M : W : C = 4 : 3 : 2, then M men, W women and C children complete 4M + 3W + 2C units in one day. For D days, multiply this result by D.
Finding the time to finish work
First express the workers in a common efficiency unit. If the total work is T units and the daily combined efficiency is E units, then days = T/E. The same method applies when workers join or leave during the task, by calculating each period separately.
Replacing one worker type with another
If one man is equivalent to w/m women, then replacing one man requires w/m women. Similarly, one woman is equivalent to m/w men. The replacement may be fractional in calculation, but the final number of workers in a practical question is generally a whole number.
Men, Women and Children Work Efficiency Data Table
Use the structured data below while following the explanation and examples.
Efficiency ratio from equal-work groups
The table shows individual efficiencies when 2 men, 3 women and 6 children complete equal work.
| Worker type | Number in equal-work group | Individual efficiency |
|---|---|---|
| Man | 2 | 3 units |
| Woman | 3 | 2 units |
| Child | 6 | 1 unit |
Note: The individual efficiency ratio is man : woman : child = 3 : 2 : 1.
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Men, Women and Children Work Efficiency Revision Points
Use these formulas and rules for quick revision.
- Equal group work does not mean equal individual efficiency; divide the common work by the number of workers.
- If aM men = bW women = cC children, then individual efficiency ratio M : W : C = bc : ac : ab.
- Total daily work equals the sum of each worker type multiplied by its individual efficiency.
- For a fixed amount of work, days = total work ÷ combined daily efficiency.
- Workers can be added only after converting their efficiencies into a common unit.
- For replacement questions, preserve the same total daily efficiency.
Men, Women and Children Work Efficiency FAQs
What is the formula for men, women and children work efficiency?
If one man, one woman and one child have efficiencies m, w and c, then work in D days by M men, W women and C children is D(Mm + Ww + Cc).
If 2 men do the same work as 3 women and 6 children, what is the efficiency ratio?
The ratio of one man, one woman and one child is 3 : 2 : 1. Hence, 1 man = 3/2 women = 3 children.
How do you find the number of women equivalent to a given number of men?
If the efficiency ratio of a man to a woman is m : w, then N men are equivalent to N × m/w women. For a 3 : 2 ratio, 4 men equal 4 × 3/2 = 6 women.
How is the completion time calculated when all three worker types work together?
Convert their efficiencies to common units, calculate combined daily work, and divide total work by it. For example, with ratio 3 : 2 : 1, 2 men, 3 women and 4 children produce 6 + 6 + 4 = 16 units per day.
Can men, women and children be added directly in a work problem?
No. Their numbers can be added only after converting them into a common efficiency unit. A man, a woman and a child represent different amounts of daily work unless their efficiencies are equal.
If 3 men equal 4 women, what is the efficiency of one woman compared with one man?
One woman has 3/4 of a man's efficiency. Therefore, 8 women are equivalent to 8 × 3/4 = 6 men.