Question

At 9 AM, train X left from station A towards station B at uniform speed of 90 km/hr. After 2 hours, train Y left from station B on a parallel track towards station A at uniform speed of 60 km/hr. If train X reached station B at 2 PM, then at what time the two trains had crossed each other?

• A. 10:48 AM
• B. 11:20 AM
• C. 12:48 PM
• D. 1:20 PM

Answer 1

The Correct Option is C

Step 1: Calculate the Total Distance 

The total distance between stations A and B is the distance traveled by Train X in 5 hours (from 9 AM to 2 PM):

\[ \text{Distance} = 90 \times 5 = 450 \text{ km} \]

Step 2: Set Up the Equation for Train Y

Train Y starts 2 hours later, so it travels for \( t - 2 \) hours. Let the time at which the trains cross be \( t \).

The distance covered by Train Y is:

\[ 60 \times (t - 2) \]

The total distance covered by both trains when they meet is 450 km:

\[ 90t = 450 - 60 \times (t - 2) \]

Step 3: Solve for \( t \)

Expanding the equation:

\[ 90t = 450 - 60t + 120 \]

\[ 150t = 570 \]

\[ t = \frac{570}{150} = 3.8 \text{ hours} \]

Final Conclusion:

The trains cross at 9 AM + 3.8 hours = 12:48 PM.

Correct answer: (C) 12:48 PM.