Correct Answer - Option 1 : 80/9 km / hr
Given:
A person covers 25% of the distance at the speed of 20 km/hr
He covers 50% of the distance at the speed of 10 km/hr
He covers remaining of the distance at the speed of 5 km/hr
Formula:
Average speed = Total distance/Total time
Calculation:
Let total distance be 100 km
25% of the distance = 100 × (25/100) = 25 km
50% of the distance = 100 × (50/100) = 50 km
Remaining distance = 100% - 25% - 50% = 25%
25% of the remaining distance = 100 × (25/100) = 25 km
Time taken by man to cover 25% of the distance at the speed of 20 km/hr = 25/20 = 5 / 4 hrs
Time taken by man to cover 50% of the distance at the speed of 10 km/hr = 50/10 ⇒ 5 hrs
Time taken by man to cover 25% of the distance at the speed of 5 km/hr = 25/5
⇒ 5 hrs
Total time = (5/4) + 5 + 5
⇒ (5/4) + 10
⇒ (45/4) hrs
∴ Average speed = 100 ÷ (45/4)
⇒ 80/9 km/hr
∴ The average speed of the person in whole journey is 80/9 km/hr
