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:

24 km

The LCM of the denominator of 2/15 and 9/20 is 60 = Total distance

He cover (2/15) × 60 = 8 unit unit by rail

He covers (9/20) × 60 = 27 unit by bus

Remaining 60 - (27 + 8) = 25 unit by cycle

25 unit = 10 km

1 unit = 2/5

60 unit = (2/5) × 60 = 24 km