work

vaibhav101 wrote:3 men, 4 women and 6 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. How many women alone can complete this work in 7 days?

A 7
B 8
C 12
D 15
E none of these

Let the rate for each child = 1 unit per day.
Since each child does half the work of a man, the rate for each man = 2 units per day.
Since each woman does double the work of a man, the rate for each woman = 4 units per day.

Combined rate for 3 men, 4 women and 6 children = (3*2) + (4*4) + (6*1) = 28 units per day.
Over 7 days, the amount of work produced by 3 men, 4 women and 6 children = rt = 7*28 units.

To complete the job in 7 days, the required rate = w/t = (7*28)/7 = 28 units per day.
Since each woman produces 4 units per day, the number of women required to produce 28 units per day = 28/4 = 7.

The correct answer is A.

vaibhav101 wrote:3 men, 4 women and 6 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. How many women alone can complete this work in 7 days?

A 7
B 8
C 12
D 15
E none of these

We can let the rate of a man = m, the rate of a woman = 2m, and the rate of a child = (1/2)m, thus:

3m + 4(2m) + 6[(1/2)m] = 1/7

3m + 8m + 3m = 1/7

14m = 1/7

m = 1/98

So the rate of a woman = 2/98 = 1/49 of the job per day.

Thus, in 7 days, a woman can complete 7 x 1/49 = 1/7 of the job. So if there are 7 women, they can complete 7 x 1/7 = 1 entire job.

Alternate Solution:

Since a child does half the work a man does, the work done by 3 men, 4 women and 6 children is equivalent to the work done by 3 + 6/2 = 6 men and 4 women. Since a woman does twice the work a man does, the work done by 6 men and 4 women is equivalent to the work done by 6/2 + 4 = 7 women. So, 7 women can complete the job in 7 days.

Answer: A