A balloon of mass 'm' is decending down with an acceleration 'a'. How much mass should be removed from it so that it starts moving up with an acceleration 'a'

Take upward direction to be the positive y-direction. If m is the mass thrown out, then the equation of motion for before and after the mass m is thrown out are Ma = F – Mg

(M–m)a = F – (M–m)g

Solving the two equations m =2ma/(a+g)