A boy travels between point A and point B at a speed of 6 km/h and returns at a speed of 9 km/h. If the total time taken by him is 1 hour 15 min, the distance between A and B is:

4.5 km

The correct answer is Option (3) → 4.5 km

Step 1: Let the distance = d km

• Speed from A → B = 6 km/h → Time = $\frac{d}{6}$​ hours
• Speed from B → A = 9 km/h → Time = $\frac{d}{9}$​ hours

Total time = 1 hour 15 minutes = 1.25 hours

$\frac{d}{6} + \frac{d}{9} = 1.25$

Step 2: Solve for d

$\text{LCM of 6 and 9 = 18}$

$\frac{3d}{18} + \frac{2d}{18} = 1.25$

$\frac{5d}{18} = 1.25$

$5d = 18 \times 1.25 = 22.5$

$d = \frac{22.5}{5} = 4.5 \, \text{km}$