A train passes an electric pole in 10 seconds and a platform 120 m long in 18 seconds. Its length in metres is :

Options

A. 150 m
B. 130 m
C. 240 m
D. 180 m

Answer

To find the length of the train, we can follow these steps:

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

### Step 2: Calculate Speed of the Train
When the train passes an electric pole (a point object), it takes 10 seconds to pass it. The distance covered in this case is equal to the length of the train. Therefore, we can express the speed of the train as:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{X}{10} \quad \text{(Equation 1)} \]

### Step 3: Calculate Total Distance When Passing the Platform
When the train passes a platform that is 120 meters long, it takes 18 seconds. The distance covered in this case is the sum of the length of the train and the length of the platform:
\[ \text{Distance} = X + 120 \]
Thus, we can express the speed again as:
\[ \text{Speed} = \frac{X + 120}{18} \quad \text{(Equation 2)} \]

### Step 4: Set the Two Speed Equations Equal
Since both expressions represent the speed of the train, we can set them equal to each other:
\[ \frac{X}{10} = \frac{X + 120}{18} \]

### Step 5: Cross Multiply to Solve for X
Cross multiplying gives us:
\[ 18X = 10(X + 120) \]
Expanding the right side:
\[ 18X = 10X + 1200 \]

### Step 6: Rearrange the Equation
Rearranging the equation to isolate \( X \):
\[ 18X - 10X = 1200 \]
\[ 8X = 1200 \]

### Step 7: Solve for X
Dividing both sides by 8:
\[ X = \frac{1200}{8} = 150 \]

### Conclusion
The length of the train is \( 150 \) meters.