Correct Answer - Option 4 : 39.13 km/h
Given:
Speed for 1st 2/5th of distance = 30 km/h
Speed for 2/3rd of the rest = 45 km/h
speed of rest 30 km = 60 km/h
Formula used:
Speed × time = Distance travelled in given time
Average speed = (Total distance travelled)/ (Total time taken)
Calculation:
Let the total distance travelled = 15x(LCM of 5 and 3)
∴ First 2/5th of distance = (2/5) × 15x
= 6x km
Distance left = 15x - 6x
= 9x
2/3rd of the rest distance = (2/3) × 9x
= 6x
Rest distance left = 30 km
∵ 6x + 6x + 30 = 15x
⇒ 15x - 12x = 30
⇒ 3x = 30
⇒ x = 10km
∴ Total distance = 15x
= 15 × 10
= 150 km
∴ Distance travelled with 30 km/h = 6x = 60 km
Time taken to travel 1st 30 km = 60km/30 km/h = 2 hrs
Distance travelled with 45 km/h = 6x = 60 km
Time taken to travel 45 km = 60km/45 km/h = 4/3 hrs
Time taken to travel last 30 km = 30km/60 km/h = 1/2 hrs
∴ Total time taken = (2 + 4/3 + 1/2) hrs
\= 23/6 hrs
∴ Average speed = 150/(23/6) km/h
= 39.13 km/h
