A stone thrown vertically up reaches three points A, B and C with velocities V/2 , V/4 and V/8 respectively. Then AB:BC is

$\text{ Using }{v}^2-u^2=2\text{ as }$

Using $v^2$-$u^2$= 2as

For AB : 

${\left(\frac{V}{4}\right)}^2-{\left(\frac{V}{2}\right)}^2=2(-g)AB$...(i)

For BC : 

${\left(\frac{v}{8}\right)}^2-{\left(\frac{v}{4}\right)}^2=2(-g)BC$..(ii)

using (i) and (ii) we get AB=4BC