Three men, four women and six children can complete a work in 7 days. ...
2 men = 1 woman
1 man =1/2 woman
3 men =3/2 women
2 children = 1 man =1/2 woman
1 child =1/4 woman
6 children =6/4 =3/2 women
Now, three men, four women and six children
=3/2 + 4 +3/2 =3+8+3/2 = 14/2 = 7 women
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Three men, four women and six children can complete a work in 7 days. ...
Given:
Three men, four women, and six children can complete a work in 7 days.
A woman does double the work a man does and a child does half the work a man does.
To find:
How many women alone can complete this work in 7 days?
Solution:
Let's assume that a man can do x units of work in a day.
Therefore, a woman can do 2x units of work in a day.
And, a child can do 0.5x units of work in a day.
Now, we can calculate the total work to be done as follows:
(3 men * x/day) + (4 women * 2x/day) + (6 children * 0.5x/day) = 1 work
⇒ (3x) + (8x) + (3x) = 1
⇒ 14x = 1
⇒ x = 1/14
So, a man can do 1/14 of the work in a day.
And, a woman can do 2/14 or 1/7 of the work in a day.
And, a child can do 0.5/14 or 1/28 of the work in a day.
Now, we can calculate how many women can complete the work in 7 days as follows:
Let's assume that n women can complete the work in 7 days.
So, the total work done by n women in 7 days is:
4 women * n * (1/7) * 7 days = n units of work
Since the total work to be done is 1 unit, we can equate the above expression to 1 and solve for n as follows:
n = 1 / (4 * 1/7) = 7
Therefore, 7 women alone can complete this work in 7 days.
Answer: Option A. 7