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3 women and 18 children together take 2 days to complete a piece of work. How many days will 9 children alone take to complete the piece of work, if 6 women alone can complete the piece of work in 3 days?
- a)9
- b)7
- c)5
- d)6
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
3 women and 18 children together take 2 days to complete a piece of w...
Since, 3 women + 18 children complete work in 2 days. Therefore, (3×2) women + (18×2) children complete work in 1 day i.e., 6 women + 36 children complete work in 1 day.
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Work of 36 children for 1 day = 1−13 = 23 [Work of 6 women for 1 day = 13]
∴ 36 children do 23 part of the work in 1 day.
36 children can do the work in 32 days.
9 children can do the work in (32×4) = 6 days.
Most Upvoted Answer
3 women and 18 children together take 2 days to complete a piece of w...
Given Data:
- 3 women and 18 children together take 2 days to complete a piece of work.
- 6 women alone can complete the piece of work in 3 days.
Calculating the work rate:
- Let the work be W.
- The work rate of 3 women and 18 children together is 1/2W per day.
- The work rate of 6 women alone is 1/3W per day.
Calculating individual work rates:
- Let the work rate of 1 woman be x.
- The work rate of 1 child will be x/6.
Equating the work rates:
- 3(x) + 18(x/6) = 1/2
- 3x + 3x = 1/2
- 6x = 1/2
- x = 1/12
Calculating the work rate of 9 children:
- Work rate of 9 children = 9(x/6) = 3x = 1/4
Calculating the time taken by 9 children:
- 9 children will take 1/(3x) days to complete the work.
- Substituting the value of x, we get:
- 9 children will take 1/(3(1/12)) = 4 days to complete the work.
Therefore, 9 children alone will take 4 days to complete the piece of work. So, the correct answer is option 'D'.
- 3 women and 18 children together take 2 days to complete a piece of work.
- 6 women alone can complete the piece of work in 3 days.
Calculating the work rate:
- Let the work be W.
- The work rate of 3 women and 18 children together is 1/2W per day.
- The work rate of 6 women alone is 1/3W per day.
Calculating individual work rates:
- Let the work rate of 1 woman be x.
- The work rate of 1 child will be x/6.
Equating the work rates:
- 3(x) + 18(x/6) = 1/2
- 3x + 3x = 1/2
- 6x = 1/2
- x = 1/12
Calculating the work rate of 9 children:
- Work rate of 9 children = 9(x/6) = 3x = 1/4
Calculating the time taken by 9 children:
- 9 children will take 1/(3x) days to complete the work.
- Substituting the value of x, we get:
- 9 children will take 1/(3(1/12)) = 4 days to complete the work.
Therefore, 9 children alone will take 4 days to complete the piece of work. So, the correct answer is option 'D'.
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3 women and 18 children together take 2 days to complete a piece of work. How many days will 9 children alone take to complete the piece of work, if 6 women alone can complete the piece of work in 3 days?a)9b)7c)5d)6Correct answer is option 'D'. Can you explain this answer?
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