Work Problem Again

[prabhu3645]

Could someone please explain me how to solve this problem, I bet it sure is easy but I cant get a grip on it.

>4 men and 3 women finish a job in 6 days, 5 men and 7 women can do the same job in 4 days. How long with 1 man and 1 woman take to finish the job.

(a) 22 (2/7) days
(b) 25 (1/2) days
(c) 5 (1/7) days
(d) 12 (7/22) days
(e) 21 (3/7) days.

[netigen]

Assume that one man does x amount of work in a day and a woman does y amount of work in a day

so the equation will be:

dx+dy = total work (where d = number of days that we have to find out)

or d = total work/ (x+y) ---> eq1

Now lets check the other info:

4 men of 6 days = 24x work
3 women for 6 days = 18y work

total work = 24x+18y ----> eq2

similarly from other info available total work = 20x+28y ----> eq3

find x = 5y/2 from eq 2 and 3

solve for d using 3 equations to get d = 156/7 or ans (A)