¹₁₀ of the visitors at a concert hall were women. 90% of the remaining visitors were men and the rest were children. The number of men was 310 more than the total number of women and children. After some men left the concert hall, 50% of the visitors that remained were men. How many men left the concert hall?

Women	Children	Men	Total
1x10	9x10		10x10
	1x9	9x9
10	9	81	100

	Women and children	Men
Before	19x1 = 19 u	81x1 = 81 u
Change		- 62 u
After	1x19 = 19 u	1x19 = 19 u

90% = ⁹⁰₁₀₀ = ⁹₁₀
Children : Men = 1 : 9

The total number of children and men at first is repeated.  Make the total number of children at first the same. LCM of 9 and 10 is 90.

50% = ⁵⁰₁₀₀ = ¹₂

When some men left, the total number of women and children remains unchanged. Make the total number of women and children the same. LCM of 19 and 1 is 19.

The number of men was 310 more than the total number of women and children at first.

Number of more men than the total number of women and children at first
= 81 u - 19 u
= 62 u

62 u = 310

1 u = 310 ÷ 62 = 5

Number of men who left the concert hall
= 81 u - 19 u
= 62 u
= 62 x 5
= 310

Answer(s): 310