Question

A train starts from Delhi at 6:00 AM and reaches Ambala Cantt at 10:00 AM. Another train starts from Ambala Cantt at 8:00 AM and reaches Delhi at 11:30 AM. If the distance between Delhi and Ambala Cantt is 200 km, 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

Hint:

Account for the 2-hour head start of the first train before setting up the meeting equation.

Answer 1

The Correct Option is A

Step 1: Find each train's speed.
Train 1 (Delhi to Ambala Cantt) covers 200 km from 6:00 AM to 10:00 AM, taking 4 hours: speed \(= \dfrac{200}{4} = 50\) km/h.
Train 2 (Ambala Cantt to Delhi) covers 200 km from 8:00 AM to 11:30 AM, taking 3.5 hours: speed \(= \dfrac{200}{3.5} = \dfrac{400}{7}\) km/h.

Step 2: Set up a common time variable.
Let \(t\) be the number of hours after 6:00 AM. Train 1's distance from Delhi at time \(t\) is \(50t\). Train 2 starts 2 hours later, at \(t=2\); for \(t\ge2\) its distance from Delhi is \(200 - \dfrac{400}{7}(t-2)\).

Step 3: Set the positions equal.
\[ 50t = 200 - \frac{400}{7}(t-2) \]
Multiplying through by 7:
\[ 350t = 1400 - 400t + 800 \]
\[ 750t = 2200 \implies t = \frac{44}{15}\text{ hours} \approx 2\text{ hours }56\text{ minutes} \]

Final Answer:
Adding 2 hours 56 minutes to the 6:00 AM start gives 8:56 AM, so option A is correct. \[ \boxed{8:56\ \text{AM}} \]