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:

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