¹₉ of the guests at a concert hall were girls. 90% of the remaining guests were boys and the rest were adults. The number of boys was 486 more than the total number of girls and adults. After some boys left the concert hall, 70% of the guests that remained were boys. How many boys left the concert hall?

Girls	Adults	Boys	Total
1x5	8x5		9x5
	1x4	9x4
5	4	36	45

	Girls and adults	Boys
Before	9x1 = 9 u	36x1 = 36 u
Change		- 15 u
After	3x3 = 9 u	7x3 = 21 u

90% = ⁹⁰₁₀₀ = ⁹₁₀
Adults : Boys = 1 : 9

The total number of adults and boys at first is repeated.  Make the total number of adults at first the same. LCM of 8 and 10 is 40.

70% = ⁷⁰₁₀₀ = ⁷₁₀

When some boys left, the total number of girls and adults remains unchanged. Make the total number of girls and adults the same. LCM of 9 and 3 is 9.

The number of boys was 486 more than the total number of girls and adults at first.

Number of more boys than the total number of girls and adults at first
= 36 u - 9 u
= 27 u

27 u = 486

1 u = 486 ÷ 27 = 18

Number of boys who left the concert hall
= 36 u - 21 u
= 15 u
= 15 x 18
= 270

Answer(s): 270