Train A completely crosses train B which is 305 m long in 24 second. If they are travelling in opposite direction and sum of speed of both are 25 m/s., then find the difference (in meter) between lengths of both trains .

Options

A. 5
B. 6
C. 8
D. 10

Explanation

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

### Step 1: Understand the problem
We need to find the difference in lengths between Train A and Train B. We know the length of Train B (305 m) and the time it takes for Train A to completely cross Train B (24 seconds). The trains are moving in opposite directions, and the sum of their speeds is given as 25 m/s.

**Hint:** Identify the known values: Length of Train B, time taken to cross, and the sum of speeds.

### Step 2: Calculate the distance covered during crossing
When Train A crosses Train B, the distance covered is equal to the length of Train B plus the length of Train A. We can express this as:
\[ \text{Distance} = \text{Length of Train A} + \text{Length of Train B} \]

Let the length of Train A be \( L_A \). Therefore:
\[ \text{Distance} = L_A + 305 \]

### Step 3: Calculate the relative speed
Since the trains are moving in opposite directions, their speeds add up. The relative speed of the two trains is given as:
\[ \text{Relative Speed} = 25 \text{ m/s} \]

### Step 4: Calculate the total distance covered in 24 seconds
Using the formula for distance:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
We can calculate the distance covered when Train A crosses Train B:
\[ \text{Distance} = 25 \text{ m/s} \times 24 \text{ s} = 600 \text{ m} \]

### Step 5: Set up the equation
Now we can set up the equation based on the distances:
\[ L_A + 305 = 600 \]

### Step 6: Solve for the length of Train A
Rearranging the equation gives us:
\[ L_A = 600 - 305 \]
\[ L_A = 295 \text{ m} \]

### Step 7: Find the difference in lengths
Now we can find the difference in lengths between Train A and Train B:
\[ \text{Difference} = |L_A - L_B| = |295 - 305| = 10 \text{ m} \]

### Final Answer
The difference in lengths between Train A and Train B is **10 meters**.

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