A train passes an electric pole in 10 sec 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 use the information given about how long it takes to pass an electric pole and a platform. Here’s the step-by-step solution:

### Step 1: Understand the Problem
The train passes an electric pole in 10 seconds and a platform that is 120 meters long in 18 seconds. We need to find the length of the train.

### Step 2: Calculate the Speed of the Train
When the train passes the electric pole, the distance it covers is equal to its own length (let's denote the length of the train as L). The speed of the train can be calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

For the electric pole:
- Distance = L (length of the train)
- Time = 10 seconds

Thus, the speed of the train (S) can be expressed as:
\[ S = \frac{L}{10} \]

### Step 3: Calculate the Speed of the Train When Passing the Platform
When the train passes the platform, it covers its own length plus the length of the platform. The total distance covered when passing the platform is:
\[ \text{Distance} = L + 120 \, \text{meters} \]
The time taken to pass the platform is 18 seconds.

Using the speed formula again:
\[ S = \frac{L + 120}{18} \]

### Step 4: Set the Two Speed Equations Equal
Since the speed of the train is the same in both scenarios, we can set the two equations for speed equal to each other:
\[ \frac{L}{10} = \frac{L + 120}{18} \]

### Step 5: Cross-Multiply to Solve for L
Cross-multiplying gives us:
\[ 18L = 10(L + 120) \]

Expanding the right side:
\[ 18L = 10L + 1200 \]

### Step 6: Rearrange the Equation
Now, rearranging the equation to isolate L:
\[ 18L - 10L = 1200 \]
\[ 8L = 1200 \]

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

### Conclusion
The length of the train is **150 meters**.

---