Question

Train A leaves station M at 7:35 AM and reaches station N at 2:35 PM on the same day. Train B leaves station N at 9:35 AM and reaches station M at 2:35 PM on the same day. Find the time when Trains A and B meet.

• A. 7:57 PM
• B. 11:18 AM
• C. 11:40 AM
• D. 7:34 AM

Answer 1

Answer:

C. 11:40 AM

Trains A and B meet at 11:40 AM.

• Find the total travel times:

  • Train A: 7:35 AM to 2:35 PM = 7 hours.

  • Train B: 9:35 AM to 2:35 PM = 5 hours.

• Assume a distance:

  • Let the distance be 35 km (LCM of 7 and 5).

  • Speed of Train A = $35 \div 7 =$ 5 km/h.

  • Speed of Train B = $35 \div 5 =$ 7 km/h.

• Calculate the head start:

  • Train A starts 2 hours earlier (7:35 AM to 9:35 AM).

  • Distance covered by Train A in 2 hours = 10 km ($5 \times 2$).

  • Remaining distance at 9:35 AM = 25 km ($35 - 10$).

• Find the meeting time:

  • Relative speed = $5 + 7 =$ 12 km/h.

  • Time to meet = $\frac{25}{12}$ hours = 2 hours and 5 minutes.

  • Meeting time = 9:35 AM + 2 hours 5 minutes = 11:40 AM.