A train of length 100 metre crosses another train of length 150 metre, running on a parallel track in the opposite direction in 9 seconds. If the speed of train having length 150 metre is 40 km/hr, then what is the speed (in km/hr) of the other train?

Options

A. 30
B. 48
C. 50
D. 60

Answer

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

### Step 1: Understand the Problem
We have two trains:
- Train A: Length = 100 meters
- Train B: Length = 150 meters
- Speed of Train B = 40 km/hr
- Time taken to cross each other = 9 seconds

We need to find the speed of Train A.

### Step 2: Calculate the Total Distance Covered
When two trains cross each other, the total distance covered is the sum of their lengths.
- Total distance = Length of Train A + Length of Train B
- Total distance = 100 m + 150 m = 250 m

### Step 3: Convert the Speed of Train B to m/s
Since we will be using the time in seconds, we should convert the speed of Train B from km/hr to m/s.
- Speed in m/s = Speed in km/hr × (1000 m / 3600 s)
- Speed of Train B = 40 km/hr × (1000 / 3600) = 40 × (5/18) = 11.11 m/s (approximately)

### Step 4: Calculate the Relative Speed of Both Trains
The relative speed of two trains moving in opposite directions is the sum of their speeds.
Let the speed of Train A be \( s_1 \) (in m/s).
- Relative speed = Speed of Train A + Speed of Train B
- Relative speed = \( s_1 + 11.11 \) m/s

### Step 5: Use the Time to Cross Each Other
We know the time taken to cross each other is 9 seconds. Using the formula:
- Distance = Speed × Time
- 250 m = (Relative speed) × Time
- 250 = (s_1 + 11.11) × 9

### Step 6: Solve for \( s_1 \)
Now, we can solve for \( s_1 \):
- 250 = 9(s_1 + 11.11)
- 250 = 9s_1 + 100
- 9s_1 = 250 - 100
- 9s_1 = 150
- \( s_1 = \frac{150}{9} \)
- \( s_1 \approx 16.67 \) m/s

### Step 7: Convert \( s_1 \) to km/hr
To convert the speed of Train A from m/s to km/hr:
- Speed in km/hr = Speed in m/s × (3600 s / 1000 m)
- Speed of Train A = 16.67 m/s × (3600 / 1000) = 16.67 × 3.6 ≈ 60 km/hr

### Final Answer
The speed of the other train (Train A) is approximately **60 km/hr**.

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