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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?
- A9
- B7
- C5
- D6
Answer not set
Discussion 1
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0
CCommunity
Solution
6 women complete a piece of work in 3 days.
Hence, one woman can complete $\frac{1}{18}$ piece of work in one day.
3 women and 18 children take 2 days to complete the work.
3 women in 2 days complete $3*2*\frac{1}{18}=\frac{1}{3}$
Hence, in two days 18 children complete $1-\frac{1}{3}=\frac{2}{3}$ of the work.
So, amount of work done by 1 child in a day is $\frac{2}{3}*\frac{1}{36}=\frac{1}{54}$
So, 9 children complete $9*\frac{1}{54}=\frac{1}{6}$ part of the work in a day.
Hence, the number of days in which 9 children alone complete the work is $6$
6 women complete a piece of work in 3 days.
Hence, one woman can complete $\frac{1}{18}$ piece of work in one day.
3 women and 18 children take 2 days to complete the work.
3 women in 2 days complete $3*2*\frac{1}{18}=\frac{1}{3}$
Hence, in two days 18 children complete $1-\frac{1}{3}=\frac{2}{3}$ of the work.
So, amount of work done by 1 child in a day is $\frac{2}{3}*\frac{1}{36}=\frac{1}{54}$
So, 9 children complete $9*\frac{1}{54}=\frac{1}{6}$ part of the work in a day.
Hence, the number of days in which 9 children alone complete the work is $6$