A train, with a uniform speed crosses a platform, 162 metres long, in 18 seconds and another platform, 120 metres long in 15 seconds. The speed of the train is

Options

A. 14km/hr
B. 42km/hr
C. 50.4 km/hr
D. 67.2 km/hr

Answer

To find the speed of the train, we will set up equations based on the information provided about the train crossing two platforms of different lengths in different times.

### Step-by-Step Solution:

1. **Define Variables:**
- Let \( L \) be the length of the train (in meters).
- Let \( X \) be the speed of the train (in meters per second).

2. **Set Up the First Equation:**
- The train crosses a platform that is 162 meters long in 18 seconds.
- The distance covered while crossing the platform is the length of the train plus the length of the platform: \( L + 162 \).
- Using the formula: Distance = Speed × Time, we can write:
\[ L + 162 = X \times 18 \]
- Rearranging gives us:
\[ L = 18X - 162 \quad \text{(Equation 1)} \]

3. **Set Up the Second Equation:**
- The train crosses another platform that is 120 meters long in 15 seconds.
- The distance covered while crossing this platform is \( L + 120 \).
- Again using the formula: Distance = Speed × Time, we have:
\[ L + 120 = X \times 15 \]
- Rearranging gives us:
\[ L = 15X - 120 \quad \text{(Equation 2)} \]

4. **Equate the Two Expressions for \( L \):**
- From Equation 1 and Equation 2, we can set them equal to each other:
\[ 18X - 162 = 15X - 120 \]

5. **Solve for \( X \):**
- Rearranging the equation:
\[ 18X - 15X = -120 + 162 \]
\[ 3X = 42 \]
\[ X = \frac{42}{3} = 14 \text{ m/s} \]

6. **Convert Speed to Kilometers per Hour:**
- To convert meters per second to kilometers per hour, we use the conversion factor \( \frac{18}{5} \):
\[ X = 14 \times \frac{18}{5} = \frac{252}{5} = 50.4 \text{ km/h} \]

### Final Answer:
The speed of the train is **50.4 km/h**.