Let 1 day task of 1 man = u
1 day task of 1 woman = v
Then we have equations :
900 u + 500 v = 1/14 [ As they complete in 14 days so 1 day work together = 1/14 ] ............(1)
1200 u + 250 v = 1 / 21
==> 2400 u + 500 v = 2 / 21 ..........(2)
Now (2) - (1) yields :
1500 u = 2/21 - 1/14
==> 1500 u = 1 / 42
==> u = 1 / (42 * 1500) is 1 man's 1 day work
So time taken by 1 man to complete work = 1500 * 42 days
= 1500 * 6 weeks
= 9000 weeks
Hence to get the work completed in 1 week :
No of men needed = 9000 / 1
= 9000
Hence 9000 should be the correct answer