A train 300 metres long is running at a speed of 90 km/hr. How many seconds will it take to cross a 200 m long train running in the opposite direction at a speed of 60 km/hr. ?

Options

A. 60 second
B. `7(1)/(5)` second
C. 12 second
D. 20 second

Answer

To solve the problem of how long it will take for a 300-meter-long train running at 90 km/hr to cross a 200-meter-long train running in the opposite direction at 60 km/hr, we can follow these steps:

### Step 1: Determine the total distance to be covered
The total distance that needs to be covered when the two trains cross each other is the sum of their lengths.

**Calculation:**
- Length of Train 1 = 300 meters
- Length of Train 2 = 200 meters
- Total Distance = Length of Train 1 + Length of Train 2 = 300 m + 200 m = 500 meters

### Step 2: Calculate the relative speed of the two trains
When two trains are moving towards each other, their speeds add up to give the relative speed.

**Calculation:**
- Speed of Train 1 = 90 km/hr
- Speed of Train 2 = 60 km/hr
- Relative Speed = Speed of Train 1 + Speed of Train 2 = 90 km/hr + 60 km/hr = 150 km/hr

### Step 3: Convert the relative speed from km/hr to m/s
To convert km/hr to m/s, we multiply by \( \frac{5}{18} \).

**Calculation:**
- Relative Speed in m/s = 150 km/hr × \( \frac{5}{18} \)
- Relative Speed in m/s = \( \frac{150 × 5}{18} = \frac{750}{18} = 41.67 \) m/s (approximately)

### Step 4: Calculate the time taken to cross each other
Using the formula for time, which is given by:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

**Calculation:**
- Time = Total Distance / Relative Speed
- Time = 500 meters / 41.67 m/s
- Time ≈ 12 seconds (approximately)

### Final Answer
It will take approximately **12 seconds** for the two trains to cross each other.

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