After striking the floor a certain ball rebounds 4/5th of its height from which it has fallen. The total distance that the ball travels before coming to rest if it is gently released from a height of 120m is

The correct option is D 1080m
$\mathrm{Initially},\mathrm{the}\mathrm{ball}\mathrm{falls}\mathrm{from}a\mathrm{height}\mathrm{of}120m.\mathrm{After}\mathrm{striking}\mathrm{the}\mathrm{floor},\mathrm{it}\mathrm{rebounds}\mathrm{and}\mathrm{goes}\mathrm{to}a\mathrm{height}\mathrm{of}\frac{4}{5}\times \left(120\right)m\mathrm{Now},\mathrm{it}\mathrm{falls}\mathrm{from}a\mathrm{height}\mathrm{of}\frac{4}{5}\times \left(120\right)m\mathrm{and}\mathrm{rebounding}\mathrm{goes}\mathrm{to}a\mathrm{height}\mathrm{of}\frac{4}{5}\left(\frac{4}{5}\right(120\left)\right)m.\mathrm{This}\mathrm{process}\mathrm{is}\mathrm{continued}\mathrm{till}\mathrm{the}\mathrm{ball}\mathrm{comes}\mathrm{to}\mathrm{rest}\mathrm{Hence},\mathrm{the}\mathrm{total}\mathrm{distance}\mathrm{travelled}\mathrm{is}D=120+2\left[\frac{4}{5}\right(120)+{\left(\frac{4}{5}\right)}^2(120)+...\infty ]\mathrm{The}\mathrm{above}\mathrm{series}\mathrm{in}\mathrm{brackets}\mathrm{is}\mathrm{an}\mathrm{infinte}\mathrm{GP}D=120+2\left(\frac{\frac{4}{5}\left(120\right)}{1-\frac{4}{5}}\right]=120+2\left(\frac{480}{1}\right]=1080m$