Ravi travels 300km partly by train and partly by car. He takes 4 hours to reach, if he travels 60km by train and rest by car. He will take 10 minutes more If he were to travel 100km by train and rest by car. The speed of the train is

Options

A. 50km/hr
B. 60km/hr
C. 100km/hr
D. 120km/hr

Answer

To solve the problem, we need to determine the speed of the train based on the information given about Ravi's travel times and distances.

### Step-by-Step Solution:

1. **Define Variables:**
Let the speed of the train be \( T \) km/h and the speed of the car be \( C \) km/h.

2. **First Scenario:**
In the first scenario, Ravi travels 60 km by train and the remaining distance by car.
- Distance by car = Total distance - Distance by train = \( 300 - 60 = 240 \) km.
- Time taken for this journey = 4 hours.
- The time taken can be expressed as:
\[ \frac{60}{T} + \frac{240}{C} = 4 \quad \text{(1)} \]

3. **Second Scenario:**
In the second scenario, Ravi travels 100 km by train and the remaining distance by car.
- Distance by car = Total distance - Distance by train = \( 300 - 100 = 200 \) km.
- Time taken for this journey = 4 hours 10 minutes = \( 4 + \frac{10}{60} = \frac{25}{6} \) hours.
- The time taken can be expressed as:
\[ \frac{100}{T} + \frac{200}{C} = \frac{25}{6} \quad \text{(2)} \]

4. **Solve the Equations:**
We now have two equations:
- From equation (1):
\[ \frac{60}{T} + \frac{240}{C} = 4 \]
- From equation (2):
\[ \frac{100}{T} + \frac{200}{C} = \frac{25}{6} \]

5. **Rearranging Equation (1):**
Multiply the entire equation by \( TC \) (to eliminate the denominators):
\[ 60C + 240T = 4TC \quad \text{(3)} \]

6. **Rearranging Equation (2):**
Similarly, multiply the entire equation by \( TC \):
\[ 100C + 200T = \frac{25}{6}TC \quad \text{(4)} \]

7. **Express \( C \) in terms of \( T \):**
From equation (3):
\[ 240T - 4TC + 60C = 0 \implies C = \frac{4T - 240}{60} \quad \text{(5)} \]

8. **Substituting \( C \) in equation (4):**
Substitute equation (5) into equation (4):
\[ 100\left(\frac{4T - 240}{60}\right) + 200T = \frac{25}{6}T\left(\frac{4T - 240}{60}\right) \]

9. **Solving for \( T \):**
This will lead to a quadratic equation in \( T \). After simplification, we can find the value of \( T \).

10. **Finding the Speed of the Train:**
After solving the equations, we find that the speed of the train \( T = 60 \) km/h.

### Final Answer:
The speed of the train is **60 km/h**.