Train A running at the speed of 108 km/hr crosses a man, who running in the opposite direction at the speed of 12 km/hr in 7.2 sec. If speed of train A increased by 25% and it takes 48 seconds to cross another train B, which running at the speed of 90 km/hr in same direction. Find the length of train B?

Options

A. A)280 meters
B. B)360 meters
C. C)180 meters
D. D)160 meters

Answer

To solve the problem step by step, we will first find the length of Train A and then use that information to find the length of Train B.

### Step 1: Find the Length of Train A
- **Given:**
- Speed of Train A = 108 km/hr
- Speed of the man = 12 km/hr
- Time taken to cross the man = 7.2 seconds

- **Convert speeds from km/hr to m/s:**
\[ \text{Speed in m/s} = \text{Speed in km/hr} \times \frac{5}{18} \]
\[ \text{Speed of Train A} = 108 \times \frac{5}{18} = 30 \text{ m/s} \]
\[ \text{Speed of the man} = 12 \times \frac{5}{18} = \frac{60}{18} = \frac{10}{3} \text{ m/s} \approx 3.33 \text{ m/s} \]

- **Relative speed when crossing the man (opposite directions):**
\[ \text{Relative speed} = \text{Speed of Train A} + \text{Speed of the man} = 30 + 3.33 = 33.33 \text{ m/s} \]

- **Using the formula:**
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
\[ \text{Length of Train A} = \text{Relative speed} \times \text{Time} = 33.33 \times 7.2 = 240 \text{ meters} \]

### Step 2: Find the New Speed of Train A
- **Increase the speed of Train A by 25%:**
\[ \text{New Speed of Train A} = 108 + \left( \frac{25}{100} \times 108 \right) = 108 + 27 = 135 \text{ km/hr} \]

- **Convert the new speed to m/s:**
\[ \text{New Speed of Train A in m/s} = 135 \times \frac{5}{18} = 37.5 \text{ m/s} \]

### Step 3: Find the Length of Train B
- **Given:**
- Speed of Train B = 90 km/hr
- Time taken to cross Train B = 48 seconds

- **Convert speed of Train B to m/s:**
\[ \text{Speed of Train B} = 90 \times \frac{5}{18} = 25 \text{ m/s} \]

- **Relative speed when crossing Train B (same direction):**
\[ \text{Relative speed} = \text{New Speed of Train A} - \text{Speed of Train B} = 37.5 - 25 = 12.5 \text{ m/s} \]

- **Using the formula for distance:**
\[ \text{Distance} = \text{Length of Train A} + \text{Length of Train B} \]
\[ \text{Length of Train A} + \text{Length of Train B} = \text{Relative speed} \times \text{Time} \]
\[ 240 + \text{Length of Train B} = 12.5 \times 48 \]
\[ 240 + \text{Length of Train B} = 600 \]
\[ \text{Length of Train B} = 600 - 240 = 360 \text{ meters} \]

### Final Answer
The length of Train B is **360 meters**.

---