Problem Solving

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

Starting point: 3 men, 4 women and 6 children

A child does half the work a man does.
In other words, 1 child = 1/2 a man
This means 6 children = 3 men
So, let's just REPLACE the 6 children with 3 men to get: 6 men and 4 women

A woman does double the work a man does
In other words, 1 man = 1/2 a woman
This means 6 men = 3 women
So, let's just REPLACE the 6 men with 3 women to get: 7 women

Answer: A

Cheers,
Brent

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