Train-A crosses a stationary train B in 35 seconds and a pole in 14 seconds with the same speed. The length of the train-A is 280 metres. What is the length of the stationary Train-B?

Options

A. 360 metres
B. 420 metres
C. 480 metres
D. 400 metres

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the Problem
We need to find the length of stationary Train B. We know the length of Train A is 280 meters, and it crosses a pole in 14 seconds and another stationary Train B in 35 seconds.

### Step 2: Calculate the Speed of Train A
To find the speed of Train A, we can use the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

Here, the distance is the length of Train A (280 meters) and the time taken to cross the pole is 14 seconds.

So, we calculate:
\[ \text{Speed of Train A} = \frac{280 \text{ meters}}{14 \text{ seconds}} = 20 \text{ meters/second} \]

### Step 3: Set Up the Equation for Crossing Train B
When Train A crosses Train B, the total distance covered is the sum of the lengths of both trains. Let the length of Train B be \( y \) meters.

The total distance covered when Train A crosses Train B is:
\[ \text{Distance} = \text{Length of Train A} + \text{Length of Train B} = 280 + y \]

### Step 4: Use the Time Taken to Cross Train B
The time taken to cross Train B is given as 35 seconds. We can use the speed we calculated earlier to set up the equation:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

Substituting the known values:
\[ 20 = \frac{280 + y}{35} \]

### Step 5: Solve for \( y \)
Now, we can solve the equation for \( y \):
1. Multiply both sides by 35:
\[ 20 \times 35 = 280 + y \]
\[ 700 = 280 + y \]

2. Rearranging gives:
\[ y = 700 - 280 \]
\[ y = 420 \]

### Conclusion
The length of the stationary Train B is **420 meters**.

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