The ratio of the first and second class fares between two railways stations is 5 : 1 and that of the number of passengers travelling by first and second classes is 1 : 50. If on a day Rs. 2,200 are collected as total fare, the amount collected from the first class passengers is

Let the first class fare and second class fare be 5x and x, respectively. Let the number of passengers travelling by first class and second class be y and 50y, respectively. Amount collected from first class passengers = 5x × y = 5xy Amount collected from second class passengers = x × 50y = 50xy Total fare collected = 5xy + 50xy = 55xy According to the question, 55xy = 2200 So, xy = 2200 ÷ 55 = 40 Amount collected from first class passengers = 5xy = 5 × 40 = Rs. 200