Lets  say that the speed of me is V1 and my friend speed is V2.  Since we both arrived  at the same times, means that it took him to path the distance that I walked for 4:05 hours (4+1/12=49/12) the same time as it took me to path the distance he walked for 2:05 hours (2+1/12=25/12)

so we can write: 49 * V1          25 *  V2
                                      ———-  =   ———-   >>>     49 * V1^2  = 25 * V2 ^2  >>>>   7 * V1  =  5 *  V2 >>>  V1 = (5/7) *V2
                                      12 * V2          12 *   V1

So now we can calculate the time after the meeting:  (49/12) * [(5/7)*V2]/V2 = 35/12 = 2+11/12 = 2:55.  So since the meeting  was at 4:05 they we both arrived at 4:05+2:55=07:00 pm

The key to the solution is that with a little bit of pencil work, it will be found, while I can walk 5 miles, my friend who started from Tumkur can walk 7 miles. Let’s assume the distance between Bangalore and Tumkur is 24 miles, then the point of meeting would be 14 miles from Bangalore, and therefore I walked 3+(3/7)miles per hour while my friend walked 4 +4/5 miles per hour, and we both arrived exactly at 7 P.M