If a student walks from his home to school at the speed of 5 km/hr, he gets late by 24 min and if he increases his speed by 4 km/hr, he reaches 24 min earlier. Find the distance between his home and school.

9 km

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

                  I               II

Speed         5      :       9

 Time          9      :      5   →   4 (Difference)

                                4   →   48 (24 mins early + 24 mins late) 

                                1   →   12 mins = \(\frac{12}{60}\) hr = \(\frac{1}{5}\) hr.

Therefore,  Distance =  speed × time = 5 × 9 × \(\frac{1}{5}\) = 9 Km