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If there were 10n women at first, there were ( 930 – 10n) men at first.

4/5 of women and 1/2 of men had left and the remaining were 1/5 of women and 1/2 of men,

10n * 1/5 + (930 – 10n) *1/2 = 360

2n + 465 – 5n = 360

3n = 105

n = 35

10n = 350

There were 350 women at first. 

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Thank you. 

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