Question

A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is,

• A. 48 km/hr
• B. 54 km/hr
• C. 66 km/hr
• D. 82 km/hr

Answer 1

The Correct Option is D

To determine the speed of the second train, we first need to calculate the relative speed of both trains as they pass each other. Since they are moving in opposite directions, we add their speeds.

Given:

• Length of first train, \( L_1 = 108 \) m
• Speed of first train, \( S_1 = 50 \) km/hr
• Length of second train, \( L_2 = 112 \) m
• Time taken to cross, \( t = 6 \) seconds

Step 1: Convert speed of the first train from km/hr to m/s.

Since \( 1 \) km/hr = \( \frac{5}{18} \) m/s, the speed of the first train in m/s is:

\[ S_1 = 50 \times \frac{5}{18} = \frac{250}{18} = 13.89 \text{ m/s} \]

Step 2: Calculate the total distance covered when the trains cross each other.

The sum of the lengths of the two trains is:

\[ L_1 + L_2 = 108 + 112 = 220 \text{ m} \]

Step 3: Use the formula for relative speed to find the speed of the second train.

The relative speed is calculated as:

\[ \text{Relative Speed} = \frac{\text{Total Distance}}{\text{Time}} = \frac{220}{6} = 36.67 \text{ m/s} \]

Now, since the relative speed is the sum of the speeds of both trains:

\[ 13.89 + S_2^{(m/s)} = 36.67 \]

Solve for \( S_2^{(m/s)} \):

\[ S_2^{(m/s)} = 36.67 - 13.89 = 22.78 \text{ m/s} \]

Step 4: Convert the speed of the second train back to km/hr.

\[ S_2^{(km/hr)} = 22.78 \times \frac{18}{5} = 82 \text{ km/hr} \]

Therefore, the speed of the second train is 82 km/hr.