A man travels 2/15 of the total journey by rail, 9/20 by car and the remaining 10 km on foot. His total journey in km is

Let the total journey be ‘x’km

Journey travelled by rail = (2/15) of x = 2x/15

Journey travelled by car = (9/20) of x = 9x/20

⇒ Journey travelled by car = 9x/20

Journey travelled on foot = total journey – (journey travelled by rail + journey travelled by car)

⇒ Journey travelled on foot $(= {\rm{x\;}} - \left( {\frac{{2x}}{{15}} + \;\frac{{9x}}{{20}}} \right))$

But journey travelled on foot = 10km

$(\therefore x - \left( {\frac{{2x}}{{15}} + \;\frac{{9x}}{{20}}} \right) = {\rm{\;}}10)$

$(\Rightarrow x - \;\left( {\frac{{8x + 27x}}{{60}}} \right) = 10)$

⇒ 60x – 35x = 600

⇒ 25x = 600

⇒ x = 24

Hence, total journey = 24 km