A man performs $$\frac{2}{15}$$ of the total journey by rail, $$\frac{9}{20}$$ by bus and the remaining 10 km, on the cycle. His total journey is :

Let the distance covered by man be x km
Journey covered by rail = $$\frac{2x}{15}$$
Journey covered by bus = $$\frac{9x}{20}$$
Remaining covered by cycle = 10 km
$$\eqalign{ & \therefore x\left( {1 - \frac{2}{{15}} - \frac{9}{{20}}} \right) = 10 \cr & \Rightarrow x\left( {\frac{{60 - 8 - 27}}{{60}}} \right) = 10 \cr & \Rightarrow x\left( {\frac{{25}}{{60}}} \right) = 10 \cr & \Rightarrow x = \frac{{10 \times 60}}{{25}} \cr & \Rightarrow x = 24{\text{ km}} \cr} $$