¹₉ of the guests at a concert hall were women. 90% of the remaining guests were men and the rest were children. The number of men was 297 more than the total number of women and children. After some men left the concert hall, 75% of the guests that remained were men. How many men left the concert hall?

Women	Children	Men	Total
1x5	8x5		9x5
	1x4	9x4
5	4	36	45

	Women and children	Men
Before	9x1 = 9 u	36x1 = 36 u
Change		- 9 u
After	1x9 = 9 u	3x9 = 27 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 8 and 10 is 40.

75% = ⁷⁵₁₀₀ = ³₄

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 9 and 1 is 9.

The number of men was 297 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
= 36 u - 9 u
= 27 u

27 u = 297

1 u = 297 ÷ 27 = 11

Number of men who left the concert hall
= 36 u - 27 u
= 9 u
= 9 x 11
= 99

Answer(s): 99