Let the distance between home and office be $`d\text{’} \; \text{km}.$
Time is taken to reach office.
- At speed of $8 \; \text{km/hr} \rightarrow 10 : 15 \; \text{AM}$
- At speed of $15 \; \text{km /hr} \rightarrow 9 : 40 \; \text{AM}$
Time difference $ = \frac{35}{60} \; \text{hr}$
$ \Rightarrow \frac{d}{8} – \frac{d}{15} = \frac{35}{60}$
$ \Rightarrow \frac{15d – 8d}{120} = \frac{35}{60}$
$ \Rightarrow 7d = 70$
$ \Rightarrow \boxed{d= 10 \; \text{km}}$
Now,
Time $ = 50 \; \text{minutes} = \frac{50}{60} = \frac{5}{6} \; \text{hr}$
Let the speed be $`S\text{’} \;\text{km/hr}$
$ \Rightarrow S = \frac{10}{\frac{5}{6}}$
$ \Rightarrow S = \frac{10 \times 6}{5}$
$ \Rightarrow \boxed{ S = 12 \; \text{km/hr}}$
$\therefore$ The required speed $ = 12 \; \text{km/hr}$
Correct Answer $: \text{C}$