A train starts from Gujrat at 3:30 pm at the speed of 90 km/hr towards Goa. After one hour another train is starts from Gujrat at the speed of 108 km/hr towards Goa. How far from Gujrat the second train will catch the first train ?

540 km

Train 2 starts after 1 hour of train 1 i.e. at 4:30 PM  with speed 108 km/hr

From 3:30 PM to 4:30 PM , only train 1 travels . so distance traveled by train 1 in 1 hour with 90 km/hr speed is  = 90 km 

Both trains move in same direction , so relative speed = ( 108 - 90 ) = 18 km/hr 

Time taken by train 2 to catch the train 1 = \(\frac{90}{18}\) = 5 hour 

Total time taken by train 1 = ( 5 + 1 ) = 6 hour 

Distance = Speed × Time 

Total distance =  90  × 6 = 540 km