Two trains 150m and 120m long respectively moving from opposite directions cross each other in 10 secs. If the speed of the second trains is 43.2 km/hr, then the speed of the first train is

Options

A. 54km/hr
B. 50km/hr
C. 52km/hr
D. 51km/hr

Answer

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

### Step 1: Understand the Problem
We have two trains moving towards each other. The lengths of the trains are 150 meters and 120 meters. They cross each other in 10 seconds. The speed of the second train is given as 43.2 km/hr. We need to find the speed of the first train.

### Step 2: Convert the Speed of the Second Train
The speed of the second train is given in kilometers per hour. We need to convert it to meters per second for consistency with the lengths of the trains.

\[ \text{Speed in m/s} = \frac{\text{Speed in km/hr} \times 1000}{3600} \]

Calculating the speed of the second train:

\[ \text{Speed of second train} = \frac{43.2 \times 1000}{3600} = \frac{43200}{3600} = 12 \text{ m/s} \]

### Step 3: Calculate the Total Distance Covered
When the two trains cross each other, the total distance covered is the sum of their lengths:

\[ \text{Total distance} = \text{Length of first train} + \text{Length of second train} = 150 \text{ m} + 120 \text{ m} = 270 \text{ m} \]

### Step 4: Use the Formula for Relative Speed
The formula for distance is:

\[ \text{Distance} = \text{Relative Speed} \times \text{Time} \]

Here, the time taken to cross each other is 10 seconds. Let the speed of the first train be \( V \) m/s. The relative speed of the two trains when moving towards each other is:

\[ \text{Relative Speed} = V + 12 \text{ m/s} \]

### Step 5: Set Up the Equation
Using the distance formula:

\[ 270 = (V + 12) \times 10 \]

### Step 6: Solve for V
Rearranging the equation:

\[ V + 12 = \frac{270}{10} \]
\[ V + 12 = 27 \]
\[ V = 27 - 12 \]
\[ V = 15 \text{ m/s} \]

### Step 7: Convert V to km/hr
To find the speed of the first train in kilometers per hour:

\[ \text{Speed in km/hr} = V \times \frac{3600}{1000} = 15 \times 3.6 = 54 \text{ km/hr} \]

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

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