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.**