I have to reach a certain place at a certain time and I find that I shall be 15 min too late, if I walk at 4 km an hour, and 10 min too soon, if I walk at 6 km an hour. How far have I to walk?

Let the distance he has to travel to reach the place = x km

and the time given to reach the place = y minutes.

If he walks 4 km in an hour he is 15 minutes late ie if he walks with a speed 4 km/hour (4km/60min)he will take y+15 minutes

distance = time*speed

ie x=$$\ \frac{\ 4}{60}$$*(y+15)

60 x = 4* (y+15)

15 x = y+15    -- Eq (1)

if he walks 6km in an hour he is 10 minutes early ie if he walks with a speed of 6km/hour he will take y-10 minutes.

x=$$\ \frac{\ 6}{60}$$ * (y-10)

10x = (y-10)    -- Eq (2)

On solving Eq 1, 2, we get

y = 60 minutes , x = 5 km

B is the correct answer.