Correct Answer - Option 2 : 6.67
Given:
1/2 part of journey is covered at the speed of = 10 km/h
1/4 part of journey is covered at the speed of = 5 km/h
And the remaining part of journey at the speed of = 5 km/h
Formula used:
Speed = Distance/Time
Calculation:
Let the total distance be = S km
According to question,
First part = S/2, Second part = S/4 and the remaining part = S – (S/2 + S/4) = S/4
time taken to cover 1/2 part of distance = (S/2)/10
⇒ S/20
Time taken to cover ¼ part of distance = (S/4)/5
⇒ S/20
And the remaining part of distance in time in = (S/4)/5
So, the total time = S/20 + S/20 + S/20 = 3S/20
So, the Average speed = total distance/ total time
Average speed = S/(3S/20)
⇒ Average speed = 20/3
∴ The average speed of the whole journey will be 6.67 km/hr
Short trick:
1/2, 1/4 take in lcm in denominator = 80 km (let total distance)
1/2 × 80 = 40, 1/4× 80 = 20
Then remaining part of distance is = 80 – (40 + 20) = 20 km
So, using the formula = speed = distance/time
⇒ 40/10 + 20/5 + 20/5 = 4 + 4 + 4 = 12 (total time)
Average speed = 80/12
∴ Average speed = 6.67
