A train passes by a lamp post on a platform in 7 sec. and passes by the platform completely in 28 sec. If the length of the platform is 390 m, then length of the train (in metres) is

Options

A. 120
B. 130
C. 140
D. 150

Answer

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

### Step 1: Define Variables
Let:
- \( L \) = length of the train (in meters)
- \( s \) = speed of the train (in meters per second)

### Step 2: Calculate Speed of the Train
The train passes a lamp post in 7 seconds. The distance it travels in this time is equal to the length of the train. Therefore, we can express the speed of the train as:
\[ s = \frac{L}{7} \]

### Step 3: Calculate Total Distance Covered When Passing the Platform
The train passes the platform completely in 28 seconds. The total distance covered in this time is the sum of the length of the train and the length of the platform. The length of the platform is given as 390 meters. Thus, the total distance can be expressed as:
\[ \text{Total Distance} = L + 390 \]
The speed can also be expressed in this scenario as:
\[ s = \frac{L + 390}{28} \]

### Step 4: Set the Two Expressions for Speed Equal
Now, we have two expressions for speed:
1. \( s = \frac{L}{7} \)
2. \( s = \frac{L + 390}{28} \)

Setting these equal to each other gives us:
\[ \frac{L}{7} = \frac{L + 390}{28} \]

### Step 5: Cross Multiply to Solve for \( L \)
Cross multiplying gives:
\[ 28L = 7(L + 390) \]

### Step 6: Expand and Rearrange the Equation
Expanding the right side:
\[ 28L = 7L + 2730 \]
Now, rearranging the equation:
\[ 28L - 7L = 2730 \]
\[ 21L = 2730 \]

### Step 7: Solve for \( L \)
Dividing both sides by 21:
\[ L = \frac{2730}{21} = 130 \]

### Conclusion
The length of the train is \( 130 \) meters.