A student goes to school at the rate of $$2\frac{1}{2}$$ km/hr and reaches 6 min late. If he travels at the speed of 3 km/hr he is 10 min early. What is the distance to the school ?

A. 4 km

B. $$3\frac{1}{4}$$ km

C. 1 km

D. $$3\frac{1}{2}$$ km

Answer: Option A

Solution(By Examveda Team)

Let the distance between school and home be = D
According to the given information :
$$\frac{D}{{2\frac{1}{2}}} - \frac{D}{3} = 16{\text{ minutes}}$$
$$\eqalign{ & \therefore \frac{{2D}}{5} - \frac{D}{3} = \frac{{16}}{{60}} \cr & \Rightarrow \frac{{6D - 5D}}{{15}} = \frac{{16}}{{60}} \cr & \Rightarrow D = \frac{{16}}{{60}} \times 15 \cr & \Rightarrow D = 4{\text{ km}} \cr} $$