Let x be the chicken and y be the number of days
This could be solved by calculating the chicken-days (cos it is a constant if we closely observe)
(x-75)(y+20) = x*y; (when 75 chicken are sold)
(x+100)(y-15) = x*y;(when 100 chicken are bought)
Since the above 2 equations are same
we get x=5y;
Solve it you get y=60 and x=300
Got 300 too, but couldn't see any short cuts here.