JEE Advanced 2020 — Paper 2 — Question 3

A hot air balloon is carrying some passengers, and a few sandbags of mass 1 kg each so that its total mass is 480 kg . Its effective volume giving the balloon its buoyancy is V. The balloon is floating at an equilibrium height of 100 m . When N number of sandbags are thrown out, the balloon rises to a new equilibrium height close to 150 m with its volume V remaining unchanged. If the variation of the density of air with height $h$ from the ground is $\rho(h)=\rho_{0} e^{-\frac{h}{h_{0}}}$, where $\rho_{0}=1.25 \mathrm{~kg} \mathrm{~m}^{-3}$ and $h_{0}=6000 \mathrm{~m}$, the value of N is $\_\_\_\_$