A student goes to school at the rate of 21/2 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 ?

Answer: Option A

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