The given situation is shown below


For Ist part of journey,
$\begin{aligned} & u=0, a=-g=-10 \mathrm{~ms}^{-2} \\ & s=-40 \mathrm{~m}\end{aligned}$
Now using, $v^2-u^2=2 a s$
we get, $\quad v^2-0=2 \times(-10)(-40)$
$\Rightarrow \quad v^2=800$...(i)
And using $v=u+a t$,
we get; $\quad v=0+a t_1$,
or $\quad v^2=a^2 t_1^2$
$\Rightarrow \quad t_1^2=\frac{v^2}{a^2}=\frac{800}{100}=8 \Rightarrow t_1=2 \sqrt{2}$
Now, for second part of journey,
$u=0, a=-10 \mathrm{~m} / \mathrm{s}^2, s=-80 \mathrm{~m}$
$\Rightarrow v^2-u^2=2 a s \Rightarrow v^2=2 \times(-10)(-80)=1600$
And $\quad v=u+a t_2$ gives,
$v=a t_2 \Rightarrow v^2=a^2 t_2^2$
Hence, $1600=100 \times t_2^2$
or $\quad t_2=4 \mathrm{~s}$
Time to complete last $50 \%$ part of the journey
$=t_2-t_1=4-2 \sqrt{2} \simeq 1.17 \mathrm{~s}$