Work And Time

[neya]

4 men,3women finish a job in 6 days and 5men,7women can do the same work in 4 days.How long will 1 men and 1 women take to do the work?

1.22(2/7)days
2.25(1/2)days
3.5(1/7) days
4.12(7/22) days

[shankar.ashwin]

Both the work done is the same,

So,

6(4M+3W) = 4(5M+7W)

2M=5W

6(13W) = Total Work.

Work done by 1M and 1W = 5/2W +W = 7/2W

78W = x(days) * 7/2W

x = 22 2/7 Days A

[GMATGuruNY]

4 men,3women finish a job in 6 days and 5men,7women can do the same work in 4 days.How long will 1 men and 1 women take to do the work?

1.22(2/7)days
2.25(1/2)days
3.5(1/7) days
4.12(7/22) days

Since 4 men + 3 women take 6 days to complete the job, 8 men + 6 women will take 3 days to complete the job.

When 8 men + 6 women are combined with 5 men + 7 women, the number of workers will be 13 men + 13 women, who will be able to produce 13 times the number of units as 1 man + 1 woman.

Let the job = LCM of 3,4, and 13 = 156 units.

Rate for 8 men + 6 women = w/t = 156/3 = 52 units per. day.
Rate for 5 men + 7 women = w/t = 156/4 = 39 units per day.
Rate for 13 men + 13 women = 52+39 = 91 units per day.
Thus, rate for 1 man + 1 woman = 91/13 = 7 units per day.
Time for 1 man + 1 woman = w/r = 156/7 ≈ 22.

The correct answer is A.