Patrol Fuel Budget Under a Hard Ceiling
A police station in Rajkot city has a monthly fuel budget of ₹30,000 for patrols. It runs two Bolero jeeps and four motorcycles. Diesel costs ₹90 per litre and a Bolero gives 12 km per litre; petrol costs ₹100 per litre and a motorcycle gives 40 km per litre. The current night patrol plan is 60 km per day for each Bolero and 40 km per day for each motorcycle, for 26 days a month. The station officer also wants to keep at least 50 km per day per Bolero and 30 km per day per motorcycle so that beat visits do not fall below the minimum. A constable claims the plan will exceed the budget by less than ₹2,000.
1. Calculate the monthly fuel cost of the current plan and test the constable's claim.
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Bolero: 60 km/day × 26 days = 1,560 km per vehicle. Fuel = 1,560 ÷ 12 = 130 litres. Cost = 130 × ₹90 = ₹11,700 per Bolero. For two Boleros: ₹23,400.
Motorcycle: 40 km/day × 26 days = 1,040 km per vehicle. Fuel = 1,040 ÷ 40 = 26 litres. Cost = 26 × ₹100 = ₹2,600 per motorcycle. For four motorcycles: ₹10,400.
Total = ₹23,400 + ₹10,400 = ₹33,800. The budget is ₹30,000, so the excess is ₹3,800. The claim that the excess is less than ₹2,000 is false.
2. If the budget cannot be raised, propose a reduced plan that still meets the minimum kilometres and stays within ₹30,000. Show the arithmetic.
Read the worked answer
Reduce the Bolero distance first because it saves more per kilometre: a Bolero costs ₹90 ÷ 12 = ₹7.50 per km, while a motorcycle costs ₹100 ÷ 40 = ₹2.50 per km.
Try Boleros at the minimum 50 km/day: 50 × 26 = 1,300 km per vehicle; 1,300 ÷ 12 = 108.33 litres; cost = 108.33 × ₹90 = ₹9,750 per vehicle; two Boleros = ₹19,500.
Keep motorcycles at 40 km/day: ₹10,400.
Total = ₹19,500 + ₹10,400 = ₹29,900, which is within ₹30,000 and leaves ₹100. Both vehicle types remain at or above the stated minimums: Boleros at 50 km/day and motorcycles at 40 km/day.
3. Diesel then rises to ₹95 per litre. Does the reduced plan still fit? If not, state the further adjustment needed.
Read the worked answer
Recalculate the Bolero cost at ₹95 per litre: 1,300 ÷ 12 = 108.33 litres per vehicle; 108.33 × ₹95 = ₹10,291.67 per vehicle; two Boleros = ₹20,583.33.
Motorcycles remain at ₹10,400. Total = ₹30,983.33, which exceeds ₹30,000 by ₹983.33. The reduced plan no longer fits.
A further adjustment is needed: either cut motorcycle distance slightly or reduce one Bolero route. Cutting motorcycle distance from 40 to 38 km/day saves: each bike does 38 × 26 = 988 km; 988 ÷ 40 = 24.7 litres; cost = ₹2,470; four bikes = ₹9,880, saving ₹520. That is not enough by itself, so a combined cut or a small budget revision is required. The station must document the shortfall rather than silently dropping below the minimum patrol distance.