# Only a single railway track is available for trains in Konkan area. A train travelling with uniform speed of 50 km per hr. leaves station ‘Ax’ at 7.40

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Only a single railway track is available for trains in Konkan area. A train travelling with uniform speed of 50 km per hr. leaves station ‘Ax’ at 7.40 am to reach the station ‘By’, which is situated at a distance of 100 km from ‘Ax’. At 8.10 am a train travelling with uniform speed of 40 km per hr. leaves station ‘By’ to reach the station ‘Ax’. The Traffic Controller noticed this situation at 8.40 am. Select the time duration that the controller has mathematically, for making decision, for avoiding collision between these two trains.
1. 20 minutes
2. 19 minutes
3. 21 minutes
4. 15 minutes

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Correct Answer - Option 1 : 20 minutes

Given:

Train travelling with uniform speed of 50 km/hr leaves station Ax to reach station By at 7:40 am.

Train travelling with uniform speed of 40 km/hr leaves station By to reach station Ax at 8:10 am.

Traffic Controller notices the situation at 8:40 am.

Calculation:

The train travelling with uniform speed of 50 km/hr leaves station 'Ax' at 7.40 am

So, time travelled till controller notices = 1 hour i.e. from 7:40 am to 8:40 am.

⇒ Distance Covered towards By till 8:40 am =  50 × 1 = 50 km

The train traveling with uniform speed of 40 km/hr leaves station 'By' At 8.10 am

So, time travelled by this train from 8:10 am to 8:40 am = 30 minutes = 0.5 hours

⇒ Distance Covered towards Ax till 8:40 am =  40 × 0.5 = 20 km

Hence total Distance Covered by both the trains = 50 + 20 = 70 km

Distance between stations = 100 km

Distance remaining between the trains at 8:40 am = 100 - 70 = 30 km

Since, both trains are moving towards each other so their relative velocity will add

⇒ Relative speed = 50 + 40 = 90 km/hr

Time left for collision = $\frac{Distance\ between\ the\ trains}{Relative\ speed}$

= (30 / 90) hrs

= 1/3 hr = 20 mins.

Hence, option 1 is correct.