Question
The cost of running a mini train is partly fixed and
partly variable. When 50 tickets are sold, the average cost per ticket is Rs. 45. When 70 tickets are sold, the average cost per ticket drops to Rs. 42. Find the average cost per ticket when 90 tickets are sold.Solution
ATQ, Let the fixed cost be Rs. 'F' and variable cost be Rs. 'V'. F + (V × 50) = 45 × 50 Or, F + 50V = 2250 .......... (I) Also, F + (V × 70) = 42 × 70 Or, F + 70V = 2940 .......... (II) On subtracting equation (I) from equation (II), we have; 20V = 690 Or, V = 34.5 On putting V = 34.5 in equation (I), we have; F + (50 × 34.5) = 2250 Or, F = 2250 − 1725 Or, F = 525 So, average cost when 90 tickets are sold: = {525 + (90 × 34.5)} ÷ 90 = 3645 ÷ 90 = Rs. 40.5
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