A passenger train running at the speed of 80 kms/hr leaves the railway station 6 hours after a goods train leaves and overtakes it in 4 hours. What is the speed of the goods train ?

Options

A. 32 kms/hr
B. 50 kms/hr
C. 45 kms/hr
D. 64 kms/hr

Answer

To solve the problem, we need to find the speed of the goods train given the information about the passenger train and the time taken for overtaking.

### Step-by-Step Solution:

1. **Identify the given information:**
- Speed of the passenger train = 80 km/hr
- The passenger train leaves 6 hours after the goods train.
- The passenger train overtakes the goods train in 4 hours.

2. **Define the speed of the goods train:**
- Let the speed of the goods train be \( x \) km/hr.

3. **Calculate the total time the goods train has been traveling when overtaken:**
- The goods train has been traveling for 6 hours (before the passenger train leaves) + 4 hours (while the passenger train is traveling) = 10 hours.

4. **Calculate the distance traveled by both trains:**
- Distance traveled by the passenger train in 4 hours:
\[ \text{Distance}_{\text{passenger}} = \text{Speed} \times \text{Time} = 80 \, \text{km/hr} \times 4 \, \text{hr} = 320 \, \text{km} \]
- Distance traveled by the goods train in 10 hours:
\[ \text{Distance}_{\text{goods}} = x \, \text{km/hr} \times 10 \, \text{hr} = 10x \, \text{km} \]

5. **Set the distances equal to each other:**
- Since both trains cover the same distance when the passenger train overtakes the goods train, we can set up the equation:
\[ 10x = 320 \]

6. **Solve for \( x \):**
- Divide both sides by 10:
\[ x = \frac{320}{10} = 32 \, \text{km/hr} \]

7. **Conclusion:**
- The speed of the goods train is \( 32 \, \text{km/hr} \).