Bus Depot Yield and Subsidy
Urban Transit Ltd operates three depots. For September it reports: Depot A has 20 lakh passengers, 25% of them AC, with average AC fare ₹40 and average non-AC fare ₹12. Depot B has 15 lakh passengers, 40% AC, average AC fare ₹45 and non-AC fare ₹10. Depot C has 25 lakh passengers, 16% AC, average AC fare ₹35 and non-AC fare ₹11. A state scheme pays ₹1 per non-AC passenger per month to any depot whose overall revenue per passenger is below ₹15. The finance officer says Depot C should receive the largest subsidy because it carries the most passengers. The operations head wants one additional conductor, costing ₹45,000 a month, posted to the depot with the highest revenue per passenger, arguing that high yield signals high fare-evasion risk.
1. Calculate revenue per passenger for each depot. Which depots qualify for the subsidy, and what is the total monthly subsidy?
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Depot A: AC passengers = 5 lakh, non-AC = 15 lakh. Revenue = 5×40 + 15×12 = 200 + 180 = 380 lakh = ₹3.80 crore. Yield = 380/20 = ₹19.00 per passenger. Not eligible.
Depot B: AC = 6 lakh, non-AC = 9 lakh. Revenue = 6×45 + 9×10 = 270 + 90 = 360 lakh = ₹3.60 crore. Yield = 360/15 = ₹24.00. Not eligible.
Depot C: AC = 4 lakh, non-AC = 21 lakh. Revenue = 4×35 + 21×11 = 140 + 231 = 371 lakh = ₹3.71 crore. Yield = 371/25 = ₹14.84. Eligible because it is below ₹15.
Only Depot C qualifies. Subsidy = 21 lakh non-AC passengers × ₹1 = ₹21 lakh per month.
2. Evaluate the finance officer's claim: 'Depot C should receive the largest subsidy because it carries the most passengers.'
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The conclusion is correct on this data but the reasoning is wrong. Depot C is the only depot with yield below ₹15, so it receives the entire subsidy. It also has the most non-AC passengers (21 lakh vs 15 lakh at A and 9 lakh at B), so its subsidy is largest.
However, the criterion is not total passengers. Eligibility depends on revenue per passenger, and the amount depends on non-AC passengers. A depot with 30 lakh passengers but a high AC share could have yield above ₹15 and receive zero. The finance officer has confused a feature that happens to be true of C with the rule that determines payment.
3. Should the additional conductor go to Depot B because it has the highest revenue per passenger? What evidence would you require?
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No. Revenue per passenger is a fare-yield measure, not an evasion measure. Depot B's ₹24 yield is explained by its 40% AC share, the highest of the three, and its high average AC fare of ₹45. That does not show that conductors are needed there.
Evasion risk is more plausibly linked to the non-AC share: C is 84% non-AC, A is 75%, and B is 60%. But even that is only a screening signal. Before posting a conductor, ask for depot-level ticketless-travel detections per 10,000 passengers, revenue-leakage audit estimates, boarding counts versus ticket sales, and peak-hour inspection data. On current data, C is the more plausible candidate, but the operations head's inference from yield is not supported.