A balloon with mass M is descending down with an acceleration a, where a < g What mass m of its contents must be removed so that it starts moving up with acceleration a? 

As shown in Figure a retarding force F acts on the balloon in the vertically upward direction and its weight mg acts in the vertically downward direction. Net force acting on the balloon in the vertically downward direction

= Mg - F

As the balloon descends down with acceleration a,

so, Mg − F = Ma     … (i)

When mass m is removed from the balloon, its net weight = (M − m)g.
Now the balloon moves with acceleration a, therefore

F − (M − m)g = (M − m)a

or Mg − Ma − (M − m)g = (M − m)a     [Using (i)]

or  Mg − Ma − Mg + mg = Ma − ma

or m(g + a) = 2Ma

or m = (2Ma) / (g + a)