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A work when done by 10 women is completed in 12 days. The same work can be completed in 8 days by 5 men. How many days will it take to complete when 6 women and 3 men are employed to perform the same job?
- a)12
- b)10
- c)8
- d)5
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A work when done by 10 women is completed in 12 days. The same work ca...
10 women complete work in 12 days
∴ 5 women complete work in 12 × 2 = 24 days
5 men can complete the same work in 8 days}
∴ Men are 3 times efficient as women
Three women can be replaced by a man
6 women and 3 men = 6/3 + 3 = 5 men
5 men can complete the work in 8 days
∴ Work is completed in 8 days
∴ 5 women complete work in 12 × 2 = 24 days
5 men can complete the same work in 8 days}
∴ Men are 3 times efficient as women
Three women can be replaced by a man
6 women and 3 men = 6/3 + 3 = 5 men
5 men can complete the work in 8 days
∴ Work is completed in 8 days
Most Upvoted Answer
A work when done by 10 women is completed in 12 days. The same work ca...
Let's first determine the rate at which each person can complete the work:
- 10 women can complete the work in 12 days, so the rate of work for 1 woman is 1/10 of the work per day.
- 5 men can complete the work in 8 days, so the rate of work for 1 man is 1/5 of the work per day.
Now, let's calculate the combined rate of work for 6 women and 3 men:
- The combined rate of work for 6 women is 6 * (1/10) = 6/10 of the work per day.
- The combined rate of work for 3 men is 3 * (1/5) = 3/5 of the work per day.
To find the total combined rate of work, we add these two rates together:
Combined rate of work = 6/10 + 3/5 = (6 + 6)/10 = 12/10 = 6/5 of the work per day.
Now, we can determine the number of days it will take to complete the work with this combined rate:
- If the combined rate of work is 6/5 of the work per day, it will take 5/6 of a day to complete 1/5 of the work.
- Therefore, it will take 5/6 * 5 = 25/6 days to complete the entire work.
Simplifying this fraction, we get:
25/6 = 4 + 1/6 = 4 + 0.1667
So, it will take approximately 4.1667 days to complete the work with 6 women and 3 men.
Since we can only select one option as the answer, we round this value to the nearest whole number, which is 4.
Therefore, the correct answer is option C) 8 days.
- 10 women can complete the work in 12 days, so the rate of work for 1 woman is 1/10 of the work per day.
- 5 men can complete the work in 8 days, so the rate of work for 1 man is 1/5 of the work per day.
Now, let's calculate the combined rate of work for 6 women and 3 men:
- The combined rate of work for 6 women is 6 * (1/10) = 6/10 of the work per day.
- The combined rate of work for 3 men is 3 * (1/5) = 3/5 of the work per day.
To find the total combined rate of work, we add these two rates together:
Combined rate of work = 6/10 + 3/5 = (6 + 6)/10 = 12/10 = 6/5 of the work per day.
Now, we can determine the number of days it will take to complete the work with this combined rate:
- If the combined rate of work is 6/5 of the work per day, it will take 5/6 of a day to complete 1/5 of the work.
- Therefore, it will take 5/6 * 5 = 25/6 days to complete the entire work.
Simplifying this fraction, we get:
25/6 = 4 + 1/6 = 4 + 0.1667
So, it will take approximately 4.1667 days to complete the work with 6 women and 3 men.
Since we can only select one option as the answer, we round this value to the nearest whole number, which is 4.
Therefore, the correct answer is option C) 8 days.
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