Ravi cycled 10 km south, turned right and cycled 5 km, then again turned right and cycled 10 km, then turned left and cycled 10 km. How far must he cycle straight to reach home?

He must cycle 15 km straight to reach home.

Start at origin; south 10 gives (0,-10).

Right faces west; 5 km gives (-5,-10).

Right faces north; 10 km gives (-5,0).

Left faces west; 10 km gives (-15,0).

The distance from (-15,0) back to the origin is 15 km.