If a student walks from his home to school at the speed of 4 km/hr, he gets late by 12 min and if he increases his speed by 3 km/hr, he reaches 12 min earlier. Find the distance between his home and school.

 \(\frac{56}{15}\) km

Distance is same, therefore speed is inversely proportional to time.

                  I               II

Speed         4      :        7

 Time          7      :      4   →   3 (Difference)

                                3   →   24 (12 mins early + 12 mins late) 

                                1   →   8 mins = \(\frac{8}{60}\) hr = \(\frac{2}{15}\) hr.

Therefore,  Distance =  speed × time = 4 × 7 × \(\frac{2}{15}\) = \(\frac{56}{15}\) Km