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If 5 men and 5 women work together then they can finish a work in 5 days but if 5 women 40 work alone then they take 3 more days than the time required by 5 men. Find efficiency of one woman is how much percentage less than one man?
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If 5 men and 5 women work together then they can finish a work in 5 da...
Given Data
- 5 men and 5 women can complete the work in 5 days.
- 5 women take 3 more days than 5 men to finish the same work.
Calculating Work Done
- Total work can be represented in terms of man-days or woman-days.
- If 5 men and 5 women complete the work in 5 days:
- Total work = (5 men + 5 women) * 5 days
- Let the efficiency of one man be M and that of one woman be W.
- Therefore, the total work is:
- Work = (5M + 5W) * 5 = 25M + 25W
Finding Individual Efficiencies
- Let the time taken by 5 men be T days.
- Hence, the time taken by 5 women is T + 3 days.
- Therefore, for 5 men:
- Work = 5M * T
- And for 5 women:
- Work = 5W * (T + 3)
Setting Equations
- Equate the total work:
- 25M + 25W = 5MT
- 25M + 25W = 5W(T + 3)
Solving for Efficiency
- From the equations, we find a relationship between M and W.
- After solving, we find:
- W = M * (3/8)
Calculating Percentage Difference
- To find how much less the efficiency of one woman is than one man:
- Difference = M - W
- Percentage less = [(M - W) / M] * 100
- Substitute W:
- Percentage less = [(M - (3/8)M) / M] * 100 = 37.5%
Conclusion
- The efficiency of one woman is 37.5% less than that of one man.
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If 5 men and 5 women work together then they can finish a work in 5 days but if 5 women 40 work alone then they take 3 more days than the time required by 5 men. Find efficiency of one woman is how much percentage less than one man?
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