Train A running at 81 km/h takes 72 sec to overtake train B, when both the trains are running in the same direction, but it takes 36 sec to cross each other if the trains are running in the opposite direction. If the length of train B is 600 metres, then find the length of train A. (in metres)

$$\eqalign{ & A + 600 = \left( {81 - s} \right) \times \frac{5}{{18}} \times 72{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {\text{i}} \right) \cr & A + 600 = \left( {81 + s} \right) \times \frac{5}{{18}} \times 36{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {{\text{ii}}} \right) \cr & {\text{From equation }}\left( {\text{i}} \right){\text{ and }}\left( {{\text{ii}}} \right) \cr & \left( {81 - s} \right) \times \frac{5}{{18}} \times 72 = \left( {81 + s} \right) \times \frac{5}{{18}} \times 36 \cr & \left( {81 - s} \right) \times 2 = \left( {81 + s} \right) \times 1 \cr & 162 - 2s = 81 + s \cr & 3s = 81 \cr & s = 27 \cr & {\text{Now, put }}s = 27{\text{ in equation }}\left( {\text{i}} \right) \cr & A + 600 = \left( {81 - 27} \right) \times \frac{5}{{18}} \times 72 \cr & A + 600 = 54 \times 20 \cr & A = 1080 - 600 \cr & A = 480{\text{ m}} \cr} $$