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Work of 2 men is equal to that of 5 women, while the work of 2 women is equal to that of 5 boys. One man alone can complete a job in 120 days. If 4 men, 10 women and 25 boys work together, in how many days would the job be completed?
- a)12
- b)10
- c)9
- d)8
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Work of 2 men is equal to that of 5 women, while the work of 2 women ...
We have, 2 Men = 5 Women; and 2 Women = 5 Boys
Thus, 4 Men = 10 Women = 25 Boys
Thus, if 4 men, 10 women and 25 boys are put together to work, it is equivalent to 12 men (4 + 4 + 4) working for the same.
Thus, if one man can complete a job in 120 days, 12 men would take 10 days to complete the same. [Using inverse proportion]
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Community Answer
Work of 2 men is equal to that of 5 women, while the work of 2 women ...
Given:
- The work of 2 men is equal to that of 5 women.
- The work of 2 women is equal to that of 5 boys.
- One man alone can complete a job in 120 days.
Let's calculate the work rate of each individual:
- The work rate of one man is 1 job in 120 days, which is 1/120 of the job per day.
- The work rate of one woman is 1/5 of the work rate of one man, which is (1/120) * (1/5) = 1/600 of the job per day.
- The work rate of one boy is 1/5 of the work rate of one woman, which is (1/600) * (1/5) = 1/3000 of the job per day.
Now, let's calculate the combined work rate of 4 men, 10 women, and 25 boys:
- The work rate of 4 men is 4 * (1/120) = 1/30 of the job per day.
- The work rate of 10 women is 10 * (1/600) = 1/60 of the job per day.
- The work rate of 25 boys is 25 * (1/3000) = 1/120 of the job per day.
Therefore, the combined work rate of all the workers is 1/30 + 1/60 + 1/120 = 1/20 of the job per day.
To find the number of days required to complete the job, we can take the reciprocal of the work rate:
Number of days = 1 / (1/20) = 20 days.
Therefore, the job will be completed in 20 days when 4 men, 10 women, and 25 boys work together.
Thus, the answer is option B) 10 days.
- The work of 2 men is equal to that of 5 women.
- The work of 2 women is equal to that of 5 boys.
- One man alone can complete a job in 120 days.
Let's calculate the work rate of each individual:
- The work rate of one man is 1 job in 120 days, which is 1/120 of the job per day.
- The work rate of one woman is 1/5 of the work rate of one man, which is (1/120) * (1/5) = 1/600 of the job per day.
- The work rate of one boy is 1/5 of the work rate of one woman, which is (1/600) * (1/5) = 1/3000 of the job per day.
Now, let's calculate the combined work rate of 4 men, 10 women, and 25 boys:
- The work rate of 4 men is 4 * (1/120) = 1/30 of the job per day.
- The work rate of 10 women is 10 * (1/600) = 1/60 of the job per day.
- The work rate of 25 boys is 25 * (1/3000) = 1/120 of the job per day.
Therefore, the combined work rate of all the workers is 1/30 + 1/60 + 1/120 = 1/20 of the job per day.
To find the number of days required to complete the job, we can take the reciprocal of the work rate:
Number of days = 1 / (1/20) = 20 days.
Therefore, the job will be completed in 20 days when 4 men, 10 women, and 25 boys work together.
Thus, the answer is option B) 10 days.
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