A man travelled distance of 42 km in 5 hours. He travelled partly on foot at the rate of 6 km/h and the rest on bicycle at the rate of 10 km/h. The distance travelled on foot is:

Answer: Option D

Let the distance travelled on foot be $$d$$
Time taken on foot + Time taken on bicycle = Total time taken
$$\begin{array}{rl}& \Rightarrow \frac{d}{6}+\frac{42-d}{10}=5\\ & \Rightarrow \frac{d\times 5+3\times \left(42-d\right)}{30}=5\\ & \Rightarrow 5d+126-3d=5\times 30\\ & \Rightarrow 2d+126=150\\ & \Rightarrow 2d=150-126\\ & \Rightarrow 2d=24\\ & \Rightarrow d=12\end{array}$$
∴ The distance travelled on foot is 12 km