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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 wo...
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.
Work of 36 children for 1 day = 
[Work of 6 women for 1 day= 1/3]
∴ 36 children do 2/3 part of the work in 1 day.
36 children can do the work in 3/2 days.
9 children can do the work in
days.
[Work of 6 women for 1 day= 1/3]∴ 36 children do 2/3 part of the work in 1 day.
36 children can do the work in 3/2 days.
9 children can do the work in
days. Most Upvoted Answer
3 women and 18 children together take 2 days to complete a piece of wo...
Given:
- 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
To find:
- How many days will 9 children alone take to complete the piece of work?
Solution:
Let us first find the work done by 1 woman in 1 day and the work done by 1 child in 1 day.
- Let the work done by 1 woman in 1 day be w.
- Let the work done by 1 child in 1 day be c.
From the given information,
- 3 women + 18 children together take 2 days to complete the work.
- So, in 1 day, they will complete 1/2 of the work.
- We can express this as:
3w + 18c = 1/2
- Also, 6 women alone can complete the work in 3 days.
- So, in 1 day, they will complete 1/18 of the work.
- We can express this as:
6w = 1/3
w = 1/18
Substituting the value of w in the first equation, we get:
3(1/18) + 18c = 1/2
1/6 + 18c = 1/2
18c = 1/2 - 1/6
18c = 1/3
c = 1/54
So, the work done by 1 child in 1 day is 1/54.
Now, let us find the number of days required for 9 children to complete the work.
- Let the number of days required be d.
- From the given information, we know that the total work done is the same in both cases (when 3 women + 18 children work together and when 9 children work alone).
- So, we can write:
(3w + 18c) x 2 = 9c x d
Substituting the values of w and c, we get:
(3 x 1/18 + 18 x 1/54) x 2 = 9 x 1/54 x d
Simplifying, we get:
d = 6
Therefore, 9 children alone will take 6 days to complete the work. Hence, the correct option is (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
To find:
- How many days will 9 children alone take to complete the piece of work?
Solution:
Let us first find the work done by 1 woman in 1 day and the work done by 1 child in 1 day.
- Let the work done by 1 woman in 1 day be w.
- Let the work done by 1 child in 1 day be c.
From the given information,
- 3 women + 18 children together take 2 days to complete the work.
- So, in 1 day, they will complete 1/2 of the work.
- We can express this as:
3w + 18c = 1/2
- Also, 6 women alone can complete the work in 3 days.
- So, in 1 day, they will complete 1/18 of the work.
- We can express this as:
6w = 1/3
w = 1/18
Substituting the value of w in the first equation, we get:
3(1/18) + 18c = 1/2
1/6 + 18c = 1/2
18c = 1/2 - 1/6
18c = 1/3
c = 1/54
So, the work done by 1 child in 1 day is 1/54.
Now, let us find the number of days required for 9 children to complete the work.
- Let the number of days required be d.
- From the given information, we know that the total work done is the same in both cases (when 3 women + 18 children work together and when 9 children work alone).
- So, we can write:
(3w + 18c) x 2 = 9c x d
Substituting the values of w and c, we get:
(3 x 1/18 + 18 x 1/54) x 2 = 9 x 1/54 x d
Simplifying, we get:
d = 6
Therefore, 9 children alone will take 6 days to complete the work. Hence, the correct option is (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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