A train with 120 wagons crosses Arun who is going in the same direction, in 36 seconds. It travels for half an hour from the time it starts overtaking the Arun ( he is riding on the horse) before it starts overtaking the Sriram( who is also riding on his horse) coming from the opposite direction in 24 seconds. In how much time (in seconds) after the train has crossed the Sriram do the Arun meets to Sriram?

Let the length of the train be L metres and speeds of the train Arun and Sriram be R, A and S respectively, then 

        $\frac{L}{R-A}=36$ ---------- (i) 

and  $\frac{L}{R+K}=24$ ---------(ii)

From eq.(i) and (ii)

              3(R - A ) = 2 (R + K) 

$\Rightarrow$  R = 3A + 2K 

In 30 minutes (i.e 1800 seconds), the train covers 1800R (distance) but the Arun also covers 1800 A (distance) in the same time. Therefore distance between Arun and Sriram, when the train has just crossed Sriram

               = 1800 ( R - A) - 24 ( A + K)

 Time required =  $\frac{1800(R-A)-24(A+K)}{(A+K)}$

= (3600 - 24) = 3576 s