Given:

Navjivan Express from Ahmedabad to Chennai leaves Ahmedabad at 6:30 am and travels at 50km/h towards Baroda

At 7.00 am Howrah-Ahmedabad Express leaves Baroda towards Ahmedabad and travels at 40 km/h

At 7:30 am Mr. Shah, the traffic controller at Baroda realizes that both trains are running on the same track

The distance between Ahmedabad to Baroda is 100 km.

Concept:

Time = Distance/Speed

Calculation:

At 7.30 AM, Distance travel by Navijan express is

⇒ 50× 1

⇒ 50 km

At 7.30 AM, Distance travel by Howrah-Ahmedabad Express is

⇒ 40× 1/2

⇒ 20 km

Now, Distance left between the both train is

⇒ 100 - 50 - 20

⇒ 30 km

Both train travel in opposite direction, then relative speed of the trains is

⇒ 50 + 40

⇒ 90 km/h

Time taken to cover this distance by both train is

⇒ 30/90

⇒ 1/3 hour = 20 min

So, He have to time less than 20 min to avert the head on collision between two trains.

∴ 15 min