Use algebra.
Let the number of stickers each had in the beginning = x stickers.
Ray lost 10 we represent this by
x - 10 ( = no. stickers he has now)
Tom bought 200 so the number of stickers he now has
= x + 200
Rays has 1/4 as much as Tom so we can now create the equation
1/4(x + 200) = x - 10
Soling for x:-
1/4 x + 50 = x - 10
60 = 3/4 x
x = 60 * 4/3 = 80
Answer they had 80 stickers at first.