A train 150 meters long crosses a milestone in 15 seconds and crosses another train of the same length travelling in the opposite direction in 12 seconds. The speed of the second train in km/hr is.
150 मी. लम्बी एक रेलगाड़ी एक पत्थर को 15 सेकेण्ड में पार कर लेती है और विपरीत दिशा में चल रही उसी लम्बाई की एक अन्य रेलगाड़ी को 12 सेकेण्ड में पार कर लेती है। दूसरी रेलगाड़ी की चाल (किमी./घंटा में) है

Options

A. A. 58 km/hr
B. B. 52 km/hr
C. C. 56 km/hr
D. D. 54 km/hr

Explanation

To solve the problem, we need to find the speed of the second train in km/hr. 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 crosses a milestone in 15 seconds.

**Formula:**
Speed = Distance / Time

**Calculation:**
- Distance = 150 meters
- Time = 15 seconds

Speed of the first train (S1) = 150 meters / 15 seconds = 10 meters/second.

### Step 2: Determine the total distance when the two trains cross each other
When the first train crosses the second train, both trains are of the same length (150 meters each). Therefore, the total distance covered when they cross each other is:

**Total Distance = Length of first train + Length of second train**
= 150 meters + 150 meters = 300 meters.

### Step 3: Calculate the relative speed of the two trains
The first train crosses the second train in 12 seconds.

**Formula:**
Relative Speed = Total Distance / Time

**Calculation:**
- Total Distance = 300 meters
- Time = 12 seconds

Relative Speed (R) = 300 meters / 12 seconds = 25 meters/second.

### Step 4: Relate the speeds of the two trains
When two trains are moving in opposite directions, the relative speed is the sum of their individual speeds.

Let the speed of the second train be S2.

**Equation:**
R = S1 + S2
25 meters/second = 10 meters/second + S2

### Step 5: Solve for the speed of the second train
Rearranging the equation gives us:

S2 = 25 meters/second - 10 meters/second = 15 meters/second.

### Step 6: Convert the speed from meters/second to kilometers/hour
To convert meters/second to kilometers/hour, we use the conversion factor (1 m/s = 18/5 km/hr).

**Calculation:**
S2 in km/hr = 15 meters/second * (18/5) = 54 km/hr.

### Final Answer
The speed of the second train is **54 km/hr**.

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