Navjivan Express from Ahmedabad to Chennai leaves Ahmedabad at 6:30 am and travels at 50kmph towards Baroda situated 100 km away. At 7.00 am Howrah-Ahmedabad Express leaves Baroda towards Ahmedabad and travels at 40 kmph. At 7:30 am Mr. Shah, the traffic controller at Baroda realizes that both trains are running on the same track. How much time does he have to avert a head-on collision between the two trains?
Step-by-step Solution:
Important Note: Based on a step-by-step calculation, the answer is 20 minutes. The provided correct option in the image (A. 15 min) appears to be incorrect. The logical method is explained below.
The goal is to determine the distance between the two trains at exactly 7:30 AM and then calculate how long it will take for them to collide from that point.
1. Position of Train 1 (Navjivan Exp.) at 7:30 AM - It starts from Ahmedabad at 6:30 AM and travels at 50 kmph.
- By 7:30 AM, it has been running for exactly 1 hour.
- Distance covered from Ahmedabad = 50 km/hr × 1 hour = 50 km.
2. Position of Train 2 (Howrah Exp.) at 7:30 AM - It starts from Baroda at 7:00 AM and travels at 40 kmph.
- By 7:30 AM, it has been running for 30 minutes (0.5 hours).
- Distance covered from Baroda = 40 km/hr × 0.5 hours = 20 km.
3. Distance Between the Trains at 7:30 AM - The total track length between Ahmedabad and Baroda is 100 km.
- Remaining distance = 100 km - (distance by T1) - (distance by T2)
- Remaining distance = 100 km - 50 km - 20 km = 30 km.
4. Time to Collision (from 7:30 AM) - The trains are moving towards each other, so their speeds add up.
- Relative Speed = 50 km/hr + 40 km/hr = 90 km/hr.
- Time = Distance ÷ Relative Speed = 30 km ÷ 90 km/hr = 1/3 hour.
- Converting to minutes: (1/3) × 60 = 20 minutes.
Conclusion: From the moment he realizes the situation at 7:30 AM, Mr. Shah has 20 minutes to avert the collision.