Two persons are walking beside a railway track at respective speeds of 2 km and 4 km per hour in the same direction. A train came from behind them and crossed them in 90 and 100 seconds, respectively. The time, in seconds, taken by the train to cross an electric post is nearest to

Let v be the speed of the train in km/h and L be its length. The relative speeds are (v-2) and (v-4) km/h. Converting to m/s, we have L = (v-2)(5/18)*90 and L = (v-4)(5/18)*100. Equating these gives 90(v-2) = 100(v-4), so 9v - 18 = 10v - 40, meaning v = 22 km/h. Substituting back, L = 20 * (5/18) * 90 = 500 meters. Time to cross a post is L/v = 500 / (22 * 5/18) = 500 * 18 / 110 = 900/11 = 81.8 seconds, which is nearest to 82.