A tourist covers half of his journey by train at 60 km/h, half of the remainder by bus at 30 km/h and the rest by cycle at 10 km/h. The average speed of the tourist in km/h during his entire journey is

Let the total distance of the journey be $D$ km.

1. First part (by train):

   • Distance $= \frac{D}{2}$

   • Speed $= 60\text{ km/h}$

   • Time taken $t_1 = \frac{D/2}{60} = \frac{D}{120}\text{ h}$

2. Second part (by bus):

   • Remainder distance $= D - \frac{D}{2} = \frac{D}{2}$

   • Distance $= \frac{1}{2} \times \frac{D}{2} = \frac{D}{4}$

   • Speed $= 30\text{ km/h}$

   • Time taken $t_2 = \frac{D/4}{30} = \frac{D}{120}\text{ h}$

3. Third part (by cycle):

   • Remaining distance $= D - \left(\frac{D}{2} + \frac{D}{4}\right) = \frac{D}{4}$

   • Speed $= 10\text{ km/h}$

   • Time taken $t_3 = \frac{D/4}{10} = \frac{D}{40}\text{ h}$

Total time taken:

Average speed:

Thus, the correct option is (C).