¹₁₀ of the people at a concert hall were women. 80% of the remaining people were men and the rest were children. The total number of women and children is 330 less than the number of men. After some men entered the concert hall, 75% of the people that remained were men. How many men entered the concert hall?

Women	Children	Men	Total
1x5	9x5		10x5
	1x9	4x9
5	9	36	50

	Women and children	Men
Before	14x1 = 14 u	36x1 = 36 u
Change		+ 6 u
After	1x14 = 14 u	3x14 = 42 u

80% = ⁸⁰₁₀₀ = ⁴₅
Children : Men = 1 : 4

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 5 is 45.

75% = ⁷⁵₁₀₀ = ³₄

When some men entered, the total number of women and children remains unchanged. Make the total number of women and children the same. LCM of 14 and 1 is 14.

The total number of women and children is 330 less than the number of men.

Number of less women and children than the number of men at first
= 36 u - 14 u
= 22 u

22 u = 330

1 u = 330 ÷ 22 = 15

Number of men who entered the concert hall
= 42 u - 36 u
= 6 u
= 6 x 15
= 90

Answer(s): 90