A train 150 m long passes a km stone in 30 seconds and another train of the same length travelling in opposite direction in 10 seconds. The speed of the second train is :

Options

A. a)90 km/hr
B. b)125 km/hr
C. c)25 km/hr
D. d)75 km/hr

Answer

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

### Step 1: Calculate the speed of the first train
The first train is 150 meters long and passes a kilometer stone (which has negligible length) in 30 seconds.

**Formula:**
Speed = Distance / Time

**Calculation:**
Speed of the first train (S1) = Length of the train / Time taken
S1 = 150 m / 30 s = 5 m/s

### Step 2: Set up the equation for the second train
The second train is also 150 meters long and is traveling in the opposite direction. When two trains cross each other, the relative speed is the sum of their speeds.

**Relative Speed Formula:**
S1 + S2 = Total distance / Time taken

Here, the total distance when the two trains cross each other is the sum of their lengths (150 m + 150 m = 300 m) and the time taken to cross each other is 10 seconds.

### Step 3: Substitute known values into the equation
We can substitute the known values into the equation:

**Equation:**
5 m/s + S2 = 300 m / 10 s

### Step 4: Solve for the speed of the second train
Now we can solve for S2:

**Calculation:**
5 + S2 = 30
S2 = 30 - 5
S2 = 25 m/s

### Step 5: Convert the speed of the second train to kilometers per hour
To convert the speed from meters per second to kilometers per hour, we use the conversion factor (1 m/s = 18/5 km/h).

**Conversion:**
Speed in km/h = Speed in m/s × (18/5)
Speed of the second train = 25 m/s × (18/5) = 90 km/h

### Final Answer:
The speed of the second train is **90 kilometers per hour**.

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