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A man and a woman can complete a work in 50 and 60 days, respectively. In how many days can 10 men and 12 women together complete the work?
- a)2
- b)2.50
- c)3
- d)4
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A man and a woman can complete a work in 50 and 60 days, respectively....
Explanation:
Given:
- Man's efficiency = 1/50
- Woman's efficiency = 1/60
Let's find the total work:
- Let the total work be represented by 'W'
- Man's work in one day = 1/50
- Woman's work in one day = 1/60
- Combined work of man and woman in one day = 1/50 + 1/60 = 6/300 + 5/300 = 11/300
- So, total work (W) = 1 (complete work) / (11/300) = 300/11
Finding the work done by 10 men and 12 women in one day:
- Work done by 10 men in one day = 10*(1/50) = 1/5
- Work done by 12 women in one day = 12*(1/60) = 1/5
- Combined work done by 10 men and 12 women in one day = 1/5 + 1/5 = 2/5
Calculating total days required by 10 men and 12 women to complete the work:
- Total work (W) = 300/11
- Work done by 10 men and 12 women in one day = 2/5
- Number of days required = Total work / Combined work done per day = (300/11) / (2/5) = (300/11) * (5/2) = 150/11 = 13.63 days (approximately)
Therefore, 10 men and 12 women together can complete the work in approximately 13.63 days, which is closest to option B (2.50).
Given:
- Man's efficiency = 1/50
- Woman's efficiency = 1/60
Let's find the total work:
- Let the total work be represented by 'W'
- Man's work in one day = 1/50
- Woman's work in one day = 1/60
- Combined work of man and woman in one day = 1/50 + 1/60 = 6/300 + 5/300 = 11/300
- So, total work (W) = 1 (complete work) / (11/300) = 300/11
Finding the work done by 10 men and 12 women in one day:
- Work done by 10 men in one day = 10*(1/50) = 1/5
- Work done by 12 women in one day = 12*(1/60) = 1/5
- Combined work done by 10 men and 12 women in one day = 1/5 + 1/5 = 2/5
Calculating total days required by 10 men and 12 women to complete the work:
- Total work (W) = 300/11
- Work done by 10 men and 12 women in one day = 2/5
- Number of days required = Total work / Combined work done per day = (300/11) / (2/5) = (300/11) * (5/2) = 150/11 = 13.63 days (approximately)
Therefore, 10 men and 12 women together can complete the work in approximately 13.63 days, which is closest to option B (2.50).
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Community Answer
A man and a woman can complete a work in 50 and 60 days, respectively....
Hence, Option B is correct.
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