$\boxed{\text{Average speed} = \frac{\text{Total distance covered}}{\text{Total time taken}}}$
Total distance covered $= 10+12 = 22 \; \text{km}$
Total time taken $= \frac{10}{12} + \frac{12}{10} = .83 + 1.2 = 2.03$
$\therefore$ Average speed $= \frac{22}{2.03} = 10.83 \; \text{km/hr}$