Fuel Arithmetic for a Rural Patrol Circle
Sub-Inspector Rekha is preparing the monthly fuel and patrol plan for a rural circle covering three police stations. The circle has 78 km of patrolling roads. Five motorcycles are available, each averaging 45 km per litre with a 12-litre tank. Each motorcycle is assigned a 26 km beat loop and is expected to complete two loops on every working day; the circle works 26 days a month. Petrol is fixed at Rs 105 per litre for the month. The district has sanctioned a monthly fuel allotment of Rs 42,000 for the circle. At the monthly crime meeting the SP wants numbers, not impressions. She is also told that from this month a home guard will ride pillion with each motorcycle on the second loop of the day, which the motor transport section says reduces mileage by 15% on the kilometres covered with a pillion. Meanwhile the station house officers complain that the allotment is 'too small for patrolling' and want it doubled.
1. Work out the monthly fuel requirement and cost of the existing two-loop plan, and state whether the sanctioned allotment is adequate.
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Step 1 - daily distance: 5 motorcycles x 2 loops x 26 km = 260 km per day.
Step 2 - monthly distance: 260 km x 26 working days = 6,760 km.
Step 3 - fuel: 6,760 / 45 km per litre = 150.22 litres.
Step 4 - cost: 150.22 x Rs 105 = Rs 15,773 (rounded).
Step 5 - compare with the allotment: Rs 42,000 buys 400 litres, so the requirement is about 37.6% of the allotment.
Conclusion: the plan is comfortably funded and the demand to double the allotment is not supported by the arithmetic. The surplus is Rs 42,000 - Rs 15,773 = Rs 26,227, which is about 249.8 litres or roughly 11,240 km of extra solo running. The correct reply to 'there is no fuel budget' is a computation placed on the file, not a silent cut in night patrols.
2. Recalculate the monthly fuel cost once the home guard rides pillion on the second loop of every day. Is the pillion escort affordable?
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Only the second loop is affected, so only half the running - 3,380 km of the 6,760 km - is covered with a pillion.
- Pillion loop: mileage falls to 45 x 0.85 = 38.25 km per litre. Fuel = 3,380 / 38.25 = 88.37 litres.
- Solo loop: fuel = 3,380 / 45 = 75.11 litres.
- Total: 163.48 litres, costing 163.48 x Rs 105 = Rs 17,165.
Extra cost over the solo plan is Rs 17,165 - Rs 15,773 = Rs 1,392 per month, about 3.3% of the allotment.
Conclusion: the pillion escort is affordable and refusing it on fuel grounds cannot be defended. Two caveats belong in the note: real mileage falls further with tyre pressure, idling at nakkas and short trips, so keep a 10% buffer; and a second rider on a motorcycle also changes the vehicle's load and handling, which is a safety instruction for the rider, not a budget question.
3. The SP asks whether a third daily loop can be added for the two highest-crime beats while keeping 10% of the allotment as an emergency reserve. Answer with figures.
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- Usable after the 10% reserve: Rs 42,000 x 0.90 = Rs 37,800.
- Already committed under the pillion plan: Rs 17,165.
- Available: Rs 37,800 - Rs 17,165 = Rs 20,635, i.e. 196.5 litres, i.e. 196.5 x 45 = 8,843 km of additional solo running.
- Cost of the third loop on two beats: 2 bikes x 26 km x 26 days = 1,352 km, which needs 1,352 / 45 = 30.04 litres, costing 30.04 x Rs 105 = Rs 3,155.
Verdict: yes. The third loop consumes only about 36% of the available surplus and leaves roughly Rs 17,480 for servicing, tyres and emergency calls.
How to make it stick: a written sanction, a logbook per motorcycle with odometer readings at every fill, a weekly comparison of litres issued against kilometres run, and a rule that any variance beyond 5% is explained by the rider in writing. In practice these plans fail not because the budget is short but because fuel is drawn without a record.