A train starts running from Delhi at 8 am and reaches Chandigarh at 11 am. While another train starts running from Chandigarh at 9 am and reach Delhi at 2 pm. At what time will they start to cross if they are running on parallel tracks?

10.15 am

Train 2 starts after 1 hour of train 1 i.e. 9 am . So, from 8 am to 9 am , only train 1 travels .

 train 1 starts running from Delhi at 8 am and reaches Chandigarh at 11 am i.e. train 1 took 3 hours  &  train 2 starts running from Chandigarh at 9 am and reach Delhi at 2 pm i.e. train 2 took 5 hours .

Ratio of          train 1    :    train 2 

time                  3        :       5

speed                5        :       3 

distance            15       :       15        ( distance = 5 × 3 = 15 ) 

Distance = Speed × Time 

for 1 hour till 9 am only train 1 travels so distance covered by it = 5R

remaining distance = 10R

As trains moves in opposite direction . so relative speed = (5 + 3 )R   =  8R 

Time taken by trains to cross each other = \(\frac{10R}{8R}\)

=  \(\frac{5}{4}\) =   \(\frac{1}{4}\)

so train will cross each other at = 9 am + 1 hour 15 minute = 10:15 am