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This is a tricky one. The key is : The total number of boys before and after the movement is the same.

Total boys = (30% x 600) + (60% x 400) = 420
Total girls = (70% X 600) + (40% x 400) = 580
Total = 1000

After movement, in team A
Boys : Girls
= 4 : 6
= 2 : 3

In team A, there are 5units of children.
In team B, there will be 1000 – 5 units of children.

Team B ratio,
Boys : Girls
= 6 : 4
= 3 : 2
= 3/5(1000 -5u) : 2/5(1000 -5u)

2u of boys in team A + 3/5(1000 – 5u) of boys in team B = 420

2u + 600 – 3u = 420
1u = 180

# of boys in team A after movement = 2u = 360
# of girls in team A after movement = 3u = 540
Total in team A = 900.

# of children transferred from team B to team A = 900 – 600 = 300.

Ref: http://www.kiasuparents.com/kiasu/forum/viewtopic.php?p=1840#p1840

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