Given that, the distance from $\text{A}$ to $ \text {B}=60\; \text{km}$
Partha and Narayan start from $\text {A}$ at the same time and move towards $\text {B}$.
Let the time taken by Narayan to reach from $\text {A}$ to $\text {B}$ be $x$ hours.
Partha takes four hours more than Narayan to reach $\text {B}$.
- The time taken by partha to reach from $ \text {A}$ to $\text{B} = (x+4)$ hours.
- The time taken by Partha to complete half of the distance $= \left ( \frac {x+4}{2} \right)$ hours.
Partha reaches the mid point of $\text {A}$ and $\text {B}$ two hours before Narayan reaches $\text {B}:$
$ x – \left(\frac {x+4}{2}\right) = 2$
$ \Rightarrow \frac {2x-(x+4)}{2} = 2$
$ \Rightarrow 2x-x-4 = 4$
$ \Rightarrow x=8 $ hours.
The time taken by Partha and Narayan to complete cover the distance from $\text {A}$ to $\text {B}:$
- Narayan time $ = x = 8\; \text{hours} $
- Partha time $ = x+4 = 8+4 = 12\; \text{hours} $
Let $S_{p}$ be the speed of partha.
Apply the formula for the speed $: \boxed {\text {Speed} =\frac{\text{Distance}} { \text{Time}}}$
$\therefore$ The speed of partha $S_{p} = \frac {60}{12} = 5 \frac { \text {km}}{ \text {h}}$
Correct Answer $: \text C$