A train passes a 60 metres long platform in 20 seconds and a man standing on the platform in 16 seconds. The speed of the train is:

Options

A. 40 kmph
B. 50 kmph
C. 38 kmph
D. 54 kmph

Answer

To find the speed of the train, we can set up equations based on the information given in the problem.

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

### Step 2: Set Up the First Equation
The train passes a 60 meters long platform in 20 seconds. The total distance covered by the train when passing the platform is the length of the train plus the length of the platform:
\[ \text{Distance} = L + 60 \]
Using the formula for speed, we have:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \implies s = \frac{L + 60}{20} \quad \text{(Equation 1)} \]

### Step 3: Set Up the Second Equation
The train passes a man standing on the platform in 16 seconds. The distance covered in this case is just the length of the train:
\[ \text{Distance} = L \]
Using the speed formula again:
\[ s = \frac{L}{16} \quad \text{(Equation 2)} \]

### Step 4: Equate the Two Expressions for Speed
Since both expressions represent the speed of the train, we can set them equal to each other:
\[ \frac{L + 60}{20} = \frac{L}{16} \]

### Step 5: Cross-Multiply to Solve for \( L \)
Cross-multiplying gives us:
\[ 16(L + 60) = 20L \]
Expanding this:
\[ 16L + 960 = 20L \]
Rearranging the equation:
\[ 960 = 20L - 16L \]
\[ 960 = 4L \]
Dividing both sides by 4:
\[ L = 240 \text{ meters} \]

### Step 6: Calculate the Speed
Now that we have the length of the train, we can substitute \( L \) back into either speed equation. Using Equation 2:
\[ s = \frac{L}{16} = \frac{240}{16} = 15 \text{ m/s} \]

### Step 7: Convert Speed to Kilometers per Hour
To convert the speed from meters per second to kilometers per hour, we multiply by 18/5:
\[ s = 15 \times \frac{18}{5} = 54 \text{ km/h} \]

### Final Answer
The speed of the train is **54 km/h**.

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