Two trains are moving in the same direction at the speed of 24 km/hr and 50 km/hr. The time taken by faster train to cross a man sitting in the slower train is 72 seconds. What will be the length (in metres) of the faster train?

Options

A. 560
B. 490
C. 520
D. 640

Answer

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

### Step 1: Identify the speeds of the trains
- The speed of the slower train (Train A) = 24 km/hr
- The speed of the faster train (Train B) = 50 km/hr

### Step 2: Calculate the relative speed
Since both trains are moving in the same direction, the relative speed is the difference in their speeds:
\[ \text{Relative Speed} = \text{Speed of Train B} - \text{Speed of Train A} = 50 \text{ km/hr} - 24 \text{ km/hr} = 26 \text{ km/hr} \]

### Step 3: Convert the relative speed to meters per second
To convert km/hr to m/s, we multiply by \(\frac{5}{18}\):
\[ \text{Relative Speed in m/s} = 26 \times \frac{5}{18} = \frac{130}{18} \approx 7.22 \text{ m/s} \]

### Step 4: Use the time taken to cross the man
The time taken by the faster train to cross a man sitting in the slower train is given as 72 seconds.

### Step 5: Calculate the length of the faster train
Using the formula:
\[ \text{Length of the train} = \text{Relative Speed} \times \text{Time} \]
Substituting the values we have:
\[ \text{Length of the faster train} = 7.22 \text{ m/s} \times 72 \text{ s} = 520 \text{ meters} \]

### Final Answer
The length of the faster train is **520 meters**.

---