Mr. tyagi while going from merrut to saharanpur covered half the distance by train at the speed of 96km/hr then the covered half of the rest distance by his scooter at the speed of 60 km/hr and finally he covered the rest distance at the speed of 40 km/hr by car. The average speed at which Mr, tyagi completed his journey is :

Options

A. 64 km/hr
B. 56 km/hr
C. 60 km/hr
D. 36 km/hr

Answer

To find the average speed of Mr. Tyagi's journey from Meerut to Saharanpur, we can follow these steps:

### Step 1: Determine the total distance
Let's assume the total distance from Meerut to Saharanpur is \( D \) kilometers. For simplicity, we can take \( D = 960 \) km, as it is a common multiple of the speeds given.

### Step 2: Calculate the distances covered in each segment
1. **Distance covered by train**:
- Half of the total distance: \( \frac{D}{2} = \frac{960}{2} = 480 \) km
2. **Distance covered by scooter**:
- Half of the remaining distance (which is also half of the total distance): \( \frac{D}{4} = \frac{960}{4} = 240 \) km
3. **Distance covered by car**:
- The remaining distance: \( \frac{D}{4} = 240 \) km

### Step 3: Calculate the time taken for each segment
1. **Time taken by train**:
- Speed = 96 km/hr
- Time = Distance / Speed = \( \frac{480}{96} = 5 \) hours
2. **Time taken by scooter**:
- Speed = 60 km/hr
- Time = Distance / Speed = \( \frac{240}{60} = 4 \) hours
3. **Time taken by car**:
- Speed = 40 km/hr
- Time = Distance / Speed = \( \frac{240}{40} = 6 \) hours

### Step 4: Calculate the total time taken
- Total time = Time by train + Time by scooter + Time by car
- Total time = \( 5 + 4 + 6 = 15 \) hours

### Step 5: Calculate the average speed
- Average speed = Total distance / Total time
- Average speed = \( \frac{960}{15} = 64 \) km/hr

Thus, the average speed at which Mr. Tyagi completed his journey is **64 km/hr**.

---