A train 150m 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. 90km/hr
B. 125km/hr
C. 25km/hr
D. 75km/hr

Answer

To solve the problem, we need to find the speed of the second train. Let's break it down step by step.

### Step 1: Calculate the speed of the first train
The first train is 150 meters long and it passes a milestone in 30 seconds.

**Formula for speed:**
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

**Distance = 150 meters** (length of the train)
**Time = 30 seconds**

So, the speed of the first train (S1) is:
\[ S1 = \frac{150 \text{ m}}{30 \text{ s}} = 5 \text{ m/s} \]

### Step 2: Set up the equation for the second train
Let the speed of the second train be S2 m/s. When the two trains are moving towards each other, their relative speed is the sum of their speeds.

**Relative speed when both trains are moving towards each other:**
\[ \text{Relative Speed} = S1 + S2 = 5 + S2 \]

### Step 3: Calculate the distance covered when both trains pass each other
When the two trains cross each other, the total distance covered is the sum of their lengths.

**Total distance = Length of first train + Length of second train = 150 m + 150 m = 300 m**

### Step 4: Use the time taken to cross each other
The second train crosses the first train in 10 seconds.

Using the formula for speed:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

We can set up the equation:
\[ 10 \text{ s} = \frac{300 \text{ m}}{(5 + S2) \text{ m/s}} \]

### Step 5: Solve for S2
Rearranging the equation gives us:
\[ 300 = 10(5 + S2) \]
\[ 300 = 50 + 10S2 \]
\[ 300 - 50 = 10S2 \]
\[ 250 = 10S2 \]
\[ S2 = \frac{250}{10} = 25 \text{ m/s} \]

### Step 6: Convert the speed from m/s to km/h
To convert m/s to km/h, we multiply by 18/5:
\[ S2 = 25 \text{ m/s} \times \frac{18}{5} = 90 \text{ km/h} \]

### Final Answer
The speed of the second train is **90 km/h**.

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