Correct Answer - Option 1 : 12 km/hr

**Given:**

Speed through cycle = 8 kmph

Speed through bus = 15 kmph

Speed through bike = 20 kmph

Speed through rickshaw = 12 kmph

**Formula used:**

Speed = Distance/Time

**Calculation:**

LCM of 4 speeds = LCM (8, 12, 15, 20)

⇒ 4 × 2 × 5 × 3 = 120

⇒ Total distance covered = 120 × 4

⇒ Total distance covered = 480 km

⇒ Time taken to travel from home to bus station = 120/8

⇒ Time taken 1 = 15 hours

⇒ Time taken to travel from bus station to B = 120/15

⇒ Time taken 2 = 8 hours

⇒ Time taken to travel on bike = 120/20

⇒ Time taken to travel on bike = 6 hours

⇒ Time taken to travel on rickshaw = 120/12

⇒ Time taken to travel on rickshaw = 10 hours

⇒ Average speed = (Total distance/4)/(Total time/4) (∵ average speed = average distance/average time)

⇒ Avg. Speed = 480/(15 + 8 + 6 + 10)

⇒ Avg. Speed = 480/39

⇒ 480/39 ≈ 12 km/hr

**∴**** Required answer is 12 km/hr.**