A balloon with its contents weighing 160 N is moving down with an acceleration of g/2 ${ ms }^{ -2 }$ the mass to be removed from it so that the balloon moves up with an acceleration of g/3${ ms }^{ -2 }$ is

Initial Weight of balloon is $160 \mathrm{~N}(16 \mathrm{~kg})$

first case

balloon move down with an acceleration $\frac{g}{2} \mathrm{~ms}^{-2}$

Let constant force acting upward on the balloon is $F$

$\begin{array}{l} 160-\mathrm{F}=16 \times \frac{\mathrm{g}}{2} \\ \Rightarrow \mathrm{F}=80 \mathrm{~N} \end{array}$

Second case

Let final mass of the balloon is $m$

balloon move upward due to force $\mathrm{F}$ with acceleration $\frac{\mathrm{g}}{3} \mathrm{~ms}^{-2}$

$\begin{array}{l} \mathrm{F}-\mathrm{mg}=\mathrm{m} \frac{\mathrm{g}}{3} \\ \Rightarrow \mathrm{F}=\frac{4 \mathrm{mg}}{3} \\ \Rightarrow 80=\frac{4 \times \mathrm{m} \times 10}{3} \\ \Rightarrow \mathrm{m}=10 \mathrm{~kg} \end{array}$

The correct option is B.