A tain crossed a 110 m long platform in 13.5 seconds and a 205 m long platform in 18.25 seconds. What was the speed of the train?

Options

A. 72 Km/h
B. 66Km/h
C. 69Km/h
D. 75 Km/h

Answer

To find the speed of the train, we will follow these steps:

### Step 1: Define Variables
Let the length of the train be \( x \) meters.

### Step 2: Set Up the First Equation
When the train crosses a 110 m long platform in 13.5 seconds, the total distance covered by the train is the length of the train plus the length of the platform, which is \( x + 110 \) meters. The time taken is 13.5 seconds.

Using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
we can express this as:
\[ x + 110 = 13.5s \quad \text{(Equation 1)} \]

### Step 3: Set Up the Second Equation
When the train crosses a 205 m long platform in 18.25 seconds, the total distance covered is \( x + 205 \) meters. The time taken is 18.25 seconds.

Using the same formula, we have:
\[ x + 205 = 18.25s \quad \text{(Equation 2)} \]

### Step 4: Equate the Two Equations
Now we have two equations:
1. \( x + 110 = 13.5s \)
2. \( x + 205 = 18.25s \)

We can set these two equations equal to each other by isolating \( x \):
From Equation 1:
\[ x = 13.5s - 110 \]
From Equation 2:
\[ x = 18.25s - 205 \]

Setting them equal to each other:
\[ 13.5s - 110 = 18.25s - 205 \]

### Step 5: Solve for \( s \)
Rearranging the equation:
\[ 205 - 110 = 18.25s - 13.5s \]
\[ 95 = 4.75s \]
\[ s = \frac{95}{4.75} \]
Calculating \( s \):
\[ s = 20 \text{ m/s} \]

### Step 6: Convert Speed to km/h
To convert the speed from meters per second to kilometers per hour, we multiply by \( 18/5 \):
\[ \text{Speed in km/h} = 20 \times \frac{18}{5} = 72 \text{ km/h} \]

### Final Answer
The speed of the train is **72 km/h**.

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