Explanation

Let the distance be x km and the scheduled travel time be t hours. Walking at 3 km/h he takes x/3 hours and arrives 40 minutes (2/3 h) early, so x/3 = t − 2/3; at 2 km/h he takes x/2 hours and arrives 2/3 h late, so x/2 = t + 2/3. Subtracting eliminates t: x/2 − x/3 = 4/3, i.e. x/6 = 4/3, giving x = 8 km. As a check, 8 km at 3 km/h takes 2 h 40 min and at 2 km/h takes 4 h — a difference of 80 minutes, exactly the 40-early/40-late spread. Hence the answer is (B) 8 km.