Walking at 3 km per hour, Pintu reaches his school 5 minutes late. If he walks at 4 km per hour he will be 5 minutes early. The distance of Pintu’s school from his house is

$$ speed = \frac{distance}{time} $$

let the distance between house and school be d

time = t

Walking at 3 km per hour, Pintu reaches his school 5 minutes late,  $$ 3 = \frac{d}{t + 5} $$..............(1)

If he walks at 4 km per hour he will be 5 minutes early, $$ 4 = \frac{d}{t - 5} $$..................(2)

from (1) and (2)

3(t + 5) = 4(t - 5)

3t + 15 = 4t - 20

solving, t = 35 minutes = $$ \frac{35}{60} =\frac{7}{12} hours $$

substitute $$ t = \frac{7}{12} in (1) $$

$$ 3 = \frac{d}{\frac{7}{12} + \frac{1}{12}} $$

solving d = 2 km