Two trains start from P and Q and head towards Q and P respectively. Train from P starts at 11 pm and reaches Q at 5 pm next day. Train fro…

Train from P starts at 11 pm and reaches Q at 5 pm next day

Time taken by train P = (5 pm next day) – 11 pm = 18 hr

Train from Q starts at 10 pm the same day on which the train starts from stationP and reaches P at 6 am the next day

Time taken by train Q = (6 am next day) – 10 pm = 8 hr

Let the distance between the station is X km

Speed of first train = Distance/Time taken to reach = X/18 km/hr

Speed of Second train = Distance/time taken to reach = X/8 km/hr

By the time the train from P starts, train from Q already travelled for (11pm – 10 pm) = 1hr

In 1 hour the train had travelled = X/8 km Now the distance between the trains = X - (X/8) = 7X/8 km

As the trains are moving in opposite direction, hence relative speed between the trains

⇒ (X/18) + (X/8) = (4X + 9X)/ 72 = 13X/72

To cover the 7X/8 km distance, it will take = $(\frac{{\frac{{7X}}{8}}}{{\frac{{13X}}{{72}}}})$ = 63/13 =4hours 11/13 × 60 min≈ 4 hours 51 minutes

So the trains will meet at (11 pm + 4 hours 51 min) ≈ 3 : 51 am