Explanation

(b) If ball falls from height $h_{1}$ and bounces back up to height $h_{2}$ then $e = \sqrt{\frac{h_{2}}{h_{1}}}$
Similarly if the velocity of ball before and after collision are $v_{1}$ and $v_{2}$ respectively then $e = \frac{v_{2}}{v_{1}}$
So $\frac{v_{2}}{v_{1}} = \sqrt{\frac{h_{2}}{h_{1}}} = \sqrt{\frac{1.8}{5}} = \sqrt{\frac{9}{25}} = \frac{3}{5}$
$i.e.$ fractional loss in velocity $= 1 - \frac{v_{2}}{v_{1}} = 1 - \frac{3}{5} = \frac{2}{5}$