A train of length 150 m takes 10 sec to pass over another train 100 m long coming from opposite direction. If the speed of the first train be 30 km/hr, the speed of the second train is

Options

A. 54 km/hr
B. 60 km/hr
C. 72 km/hr
D. 36 km/hr

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 = 150 m) moving at a speed of 30 km/hr.
- Train B (length = 100 m) moving in the opposite direction with an unknown speed (let's denote it as x km/hr).

### Step 2: Convert the Speed of Train A
The speed of Train A is given in km/hr, and we need to convert it to m/s for consistency in units.
- Speed in m/s = Speed in km/hr × (5/18).
- Therefore, the speed of Train A in m/s = 30 × (5/18) = (150/18) m/s = 25/3 m/s.

### Step 3: Calculate the Total Length of Both Trains
When both trains pass each other, the total distance covered is the sum of their lengths.
- Total length = Length of Train A + Length of Train B = 150 m + 100 m = 250 m.

### Step 4: Determine the Relative Speed
Since the trains are moving in opposite directions, their relative speed is the sum of their speeds.
- Relative speed = Speed of Train A + Speed of Train B = (25/3) + (x × (5/18)) m/s.

### Step 5: Use the Time Taken to Pass Each Other
The time taken for Train A to pass Train B is given as 10 seconds.
- Distance = Speed × Time.
- Therefore, 250 m = (Relative Speed) × (Time).
- Substitute the values:
\[ 250 = \left(\frac{25}{3} + \frac{5x}{18}\right) \times 10. \]

### Step 6: Simplify the Equation
- Divide both sides by 10:
\[ 25 = \frac{25}{3} + \frac{5x}{18}. \]
- Multiply through by 18 to eliminate the fraction:
\[ 450 = 150 + 5x. \]

### Step 7: Solve for x
- Rearranging the equation gives:
\[ 5x = 450 - 150, \]
\[ 5x = 300. \]
- Dividing both sides by 5:
\[ x = 60 \text{ km/hr}. \]

### Final Answer
The speed of the second train is **60 km/hr**.

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