Question

A train starts from Delhi at 6 : 00 AM and reaches Ambala Cantt at 10 AM. The other train starts from Ambala Cantt at 8 AM and reaches Delhi at 11:30 AM. If the distance between Delhi and Ambala Cantt. is 200 km, then at what time did the two trains meet each other ?

• A. 8 : 56 AM
• B. 8 : 46 AM
• C. 7 : 56 AM
• D. 8 : 30 AM

Answer 1

The Correct Option is A

To solve this problem, we first calculate the speeds of both trains:

• The first train travels from Delhi to Ambala Cantt from 6:00 AM to 10:00 AM, which is 4 hours. Given that the distance is 200 km, the speed of the first train is:
  Speed of Train 1 = $\frac{200}{4}$ = 50 km/h
• The second train travels from Ambala Cantt to Delhi from 8:00 AM to 11:30 AM, which is 3.5 hours. Its speed is:
  Speed of Train 2 = $\frac{200}{3.5}$ = $\frac{400}{7}$ ≈ 57.14 km/h

Next, to find the meeting time, we analyze their journey:

• The first train has already been traveling for 2 hours before the second train starts at 8:00 AM, covering a distance of 100 km (2 hours × 50 km/h).
• They will meet when their combined distances cover 200 km. Denoting t as the time after 8:00 AM, we equate:
  $50t\; +\; 100\; +\frac{400}{7}t=\; 200$
• Solving this equation:
  $50t\; +\frac{400}{7}t=\; 100$

• Combining terms:
  $\frac{\mathrm{750t}}{14}=\; 100$
• Solving for t:
  $t\; =\frac{\mathrm{100\; \times \; 14}}{750}=\frac{1400}{750}=\frac{56}{30}$ or $t\; =\frac{28}{15}$
• Converting t into minutes: $\frac{28}{15}\times \; 60\; =\; 112$ minutes or 1 hour and 52 minutes

Adding 1 hour and 52 minutes to 8:00 AM results in the meeting time being 8:56 AM.