Finding The Time Of Arrival

What was the puzzle? 

Let 'x' km/minute be the speed of Rohit's walk. He started to walk at 12 PM & met Samit at 4:05 PM. That means he has walked for 245 minutes. 

Distance traveled by Rohit = 245x km

Let 'y' km/minute be the speed of Samit's walk. He started to walk at 2 PM & met Samit at 4:05 PM. That means he has walked for 125 minutes.

Distance traveled by Samit = 125y km 

    Time of Meeting

Now after meeting each other they resumed their journey further. That means Rohit continues to Tumkur & covers distance of 125y km at his speed of x km/minute. Time taken by him further to complete the journey is 125y / x minutes (Time = Distance/Speed).

Similarly, Samit need to travel 245x km to reach Bangalore at speed of y km/minute. So he took time 245x / y minutes to reach the destination.

Since both reached at the same time at their respective destinations after meeting each other at 4:05 PM, time taken by them to complete rest of journey must be equal.

Hence,

125y / x = 245 x / y

245 x^2 = 125 y^2

x^2 / y^2 = 125 / 245 = 25 / 49

x / y = 5 / 7

Now, we have ratio of x / y which we can put in 'time' taken by Rohit & Samit.

So Rohit took 125 y / x = 125 * ( 7 / 5) = 175 minutes to reach Tumkur & obviously Samit required 245 x / y = 245 * ( 5 / 7) = 175 minutes.

To conclude, after meeting each other at 4:05 PM both reached at their respective destination in 175 minutes = 2 hours 55 minutes i.e. at 7 PM