A constant upward buoyancy force B is exerted by the atmosphere on...

Let the air resistance be $kv$.

When the balloon falls with a constant velocity $v$, the air resistance acts upwards. Equating the forces for zero net force:

$Mg = B + kv$

$kv = Mg - B$

Let $M'$ be the new mass of the balloon when it rises with the same constant speed $v$. The air resistance now acts downwards. Equating the forces:

$B = M'g + kv$

Substituting the value of $kv$ from the first equation:

$B = M'g + (Mg - B)$

$M'g = 2B - Mg$

$M' = \dfrac{2B}{g} - M$

The amount of mass that must be removed is:

$\Delta M = M - M'$

\Delta M = M - \left(\dfrac{2B}{g} -M\right)$<br><br>$\Delta M = 2M - $\dfrac{2B}{g} =$2 \left(M - \dfrac{B}{g}\right)