A man covers a total distance of 100 km on bicycle. For the first 2 hours, the speed was 20 km/hr and for the rest of the journey, it came down to 10 km/hr. The average speed will be :

Options

A. `12 (1)/(2)` km/hr
B. 13 km/hr
C. `15 (1)/(8)` km/hr
D. 20 km/hr

Answer

To find the average speed of the man who covers a total distance of 100 km on a bicycle, we can follow these steps:

### Step 1: Calculate the distance covered in the first part of the journey.
The man travels for the first 2 hours at a speed of 20 km/hr.

**Distance = Speed × Time**
Distance covered in the first 2 hours = 20 km/hr × 2 hours = 40 km.

### Step 2: Determine the remaining distance.
The total distance is 100 km, and the distance covered in the first part is 40 km.

Remaining distance = Total distance - Distance covered in the first part
Remaining distance = 100 km - 40 km = 60 km.

### Step 3: Calculate the time taken to cover the remaining distance.
The speed for the remaining part of the journey is 10 km/hr.

**Time = Distance / Speed**
Time taken to cover the remaining 60 km = 60 km / 10 km/hr = 6 hours.

### Step 4: Calculate the total time taken for the entire journey.
Total time taken = Time for the first part + Time for the second part
Total time taken = 2 hours + 6 hours = 8 hours.

### Step 5: Calculate the average speed.
Average speed is defined as the total distance divided by the total time taken.

**Average Speed = Total Distance / Total Time**
Average Speed = 100 km / 8 hours = 12.5 km/hr or 12 1/2 km/hr.

### Final Answer:
The average speed of the man is 12.5 km/hr.

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