¹₁₀ of the people at a park were girls. 90% of the remaining people were boys and the rest were adults. The number of boys was 682 more than the total number of girls and adults. After some boys left the park, 50% of the people that remained were boys. How many boys left the park?

Girls	Adults	Boys	Total
1x10	9x10		10x10
	1x9	9x9
10	9	81	100

	Girls and adults	Boys
Before	19x1 = 19 u	81x1 = 81 u
Change		- 62 u
After	1x19 = 19 u	1x19 = 19 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 9 and 10 is 90.

50% = ⁵⁰₁₀₀ = ¹₂

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 19 and 1 is 19.

The number of boys was 682 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
= 81 u - 19 u
= 62 u

62 u = 682

1 u = 682 ÷ 62 = 11

Number of boys who left the park
= 81 u - 19 u
= 62 u
= 62 x 11
= 682

Answer(s): 682