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40 men and 20 women together can complete a work in 12 days and ratio of efficiency of a man to a woman is 2:3, find how many men are required to complete half of the work in 7 days?
- a)70
- b)35
- c)30
- d)60
- e)45
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
40 men and 20 women together can complete a work in 12 days and ratio ...
Understanding the Problem
To solve the problem, first, we need to understand the total work done by 40 men and 20 women in 12 days.
Calculating Total Work
- Let the efficiency of a man be 2 units and a woman be 3 units.
- Total efficiency of 40 men = 40 * 2 = 80 units.
- Total efficiency of 20 women = 20 * 3 = 60 units.
- Combined efficiency = 80 + 60 = 140 units per day.
Now, the total work done in 12 days:
- Total work = Efficiency × Time = 140 units/day × 12 days = 1680 units.
Half of the Work
- Since we need to find out how many men are required to complete half of the work in 7 days:
- Half of the work = 1680 units / 2 = 840 units.
Setting Up the Equation
Let the number of men required be \( x \).
- Efficiency of \( x \) men = \( 2x \) units.
- Total work done by \( x \) men in 7 days = \( 7 × 2x = 14x \).
Set the equation for half the work:
- \( 14x = 840 \)
Solving for \( x \)
- \( x = 840 / 14 = 60 \).
Conclusion
Thus, **60 men** are required to complete half of the work in 7 days. Therefore, the correct answer is option **D**.
To solve the problem, first, we need to understand the total work done by 40 men and 20 women in 12 days.
Calculating Total Work
- Let the efficiency of a man be 2 units and a woman be 3 units.
- Total efficiency of 40 men = 40 * 2 = 80 units.
- Total efficiency of 20 women = 20 * 3 = 60 units.
- Combined efficiency = 80 + 60 = 140 units per day.
Now, the total work done in 12 days:
- Total work = Efficiency × Time = 140 units/day × 12 days = 1680 units.
Half of the Work
- Since we need to find out how many men are required to complete half of the work in 7 days:
- Half of the work = 1680 units / 2 = 840 units.
Setting Up the Equation
Let the number of men required be \( x \).
- Efficiency of \( x \) men = \( 2x \) units.
- Total work done by \( x \) men in 7 days = \( 7 × 2x = 14x \).
Set the equation for half the work:
- \( 14x = 840 \)
Solving for \( x \)
- \( x = 840 / 14 = 60 \).
Conclusion
Thus, **60 men** are required to complete half of the work in 7 days. Therefore, the correct answer is option **D**.
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Community Answer
40 men and 20 women together can complete a work in 12 days and ratio ...
work rate of men =2x
Work rate of women = 3x
Total work done in 12 days = (40*2x(men's Work) + 20*3x(women's Work))*12
Half work to be done by men in 7 days will be equal to =(140*12x/7)*1/2x(men's Work rate)*1/2(Half work)
gives 60 Men
Answer D.
Work rate of women = 3x
Total work done in 12 days = (40*2x(men's Work) + 20*3x(women's Work))*12
Half work to be done by men in 7 days will be equal to =(140*12x/7)*1/2x(men's Work rate)*1/2(Half work)
gives 60 Men
Answer D.
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40 men and 20 women together can complete a work in 12 days and ratio of efficiency of a man to a woman is 2:3, find how many men are required to complete half of the work in 7 days?a)70b)35c)30d)60e)45Correct answer is option 'D'. Can you explain this answer?
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