Rahul has to travel $1\frac{ 1}{4}$ km to reach school. What distance does he travel to go to school and come back?

Given:
Distance between school and home $=1\frac{1}{4}km=\frac{5}{4}km$

To find:
Total distance travelled by Rahul

Calculation:
$$\begin{gathered} \mathrm{Total} \mathrm{distance}=2\times \mathrm{distance} \mathrm{between} \mathrm{school} \mathrm{and} \mathrm{home} \\ =2\times \frac{5}{4}=\frac{5}{2} \\ =2\frac{1}{2}\mathrm{km} \end{gathered}$$

Hence, correct answer is Option C.