A boy walked a certain distance. One –fourth of the distance he walked at 10 km per hr. another one-fourth of the distance he waked at 20km per hr. and the rest at 30km per hr. find his average speed.

Correct option is C

​Let the total distance walked by the boy be D.
- One-fourth of the distance is walked at 10 km/h, so the distance covered at 10 km/h is D/4.
- One-fourth of the distance is walked at 20 km/h, so the distance covered at 20 km/h is D/4.
- The remaining half of the distance, i.e., D/2, is covered at 30 km/h.
Now, let’s calculate the time taken for each part of the journey:

1. Time taken to cover D/4 at 10 km/h:
Time_1 = (D/4) / 10 = D / 40
2. Time taken to cover D/4 at 20 km/h:
Time_2 = (D/4) / 20 = D / 80
3. Time taken to cover D/2 at 30 km/h:
Time_3 = (D/2) / 30 = D / 60

Now, the total time taken for the journey is the sum of the times for each part:
Total Time = D/40 + D/80 + D/60

To add these, first find the least common denominator (LCD), which is 240:
D/40 = 6D/240, D/80 = 3D/240, D/60 = 4D/240
So, the total time is:
Total Time = 6D/240 + 3D/240 + 4D/240 = 13D/240

The average speed is given by the total distance divided by the total time:
Average Speed = D / (13D/240) = 240 / 13  km/h

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