Question
The cost of booking a bus consists of a fixed charge and
a variable charge per seat. When 75 seats are booked, the average cost per seat is Rs. 36. However, if 90 seats are booked, the average cost per seat decreases to Rs. 35. Determine the average cost per seat when 100 seats are booked.Solution
Let the fixed cost of booking be Rs. 'F' and variable cost be Rs. 'V'. F + (V X 75) = 36 X 75 Or, F + 75V = 2700 .......... (I) Also, F + (V X 90) = 35 X 90 Or, F + 90V = 3150 ........ (II) On subtracting equation (I) from equation (II) , we have; 15V = 450 Or, 'V' = 30 On putting 'V' = 30 in equation (I) , we have; F + (75 X 30) = 2700 Or, F = 2700 - 2250 Or, 'F' = 450 So, average fare when 100 seats are booked: = {450 + (100 X 30) } ÷ 100 = (3450/100) = Rs. 34.5
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