Fuel Rationing for Night Beats at Kothapalli Police Station
The Kothapalli rural police station runs night beats with three Bolero jeeps. Each jeep covers a 120 km beat on every night it is deployed. Jeep A is deployed 6 nights a week, jeep B 6 nights a week and jeep C 5 nights a week, and the station budgets on exactly 4 weeks in a month. On the beat route the jeeps average 12 km per litre (A), 9 km per litre (B) and 10 km per litre (C). Diesel at the local pump costs ₹94.50 a litre. The station's monthly allotment from the district is 720 litres, and any excess must be bought from the district welfare fund at ₹100 a litre. The station house officer has been told to keep next month's consumption inside 720 litres without cancelling a single beat night. He is considering either shifting nights from jeep B to jeep A, or covering some of B's nights by motorcycle, which returns 35 km per litre.
1. Work out the monthly diesel requirement of each jeep, the total consumption, the excess over the allotment, and the cost of buying that excess from the district welfare fund.
Read the worked answer
Step 1 - kilometres per month
- A: 120 km × 6 nights × 4 weeks = 2,880 km
- B: 120 × 6 × 4 = 2,880 km
- C: 120 × 5 × 4 = 2,400 km
Step 2 - litres at each jeep's own mileage
- A: 2,880 ÷ 12 = 240 L
- B: 2,880 ÷ 9 = 320 L
- C: 2,400 ÷ 10 = 240 L
Step 3 - total and gap 240 + 320 + 240 = 800 L. Allotment 720 L, so the excess is 80 L.
Step 4 - cost The excess is bought at the fund rate, so 80 × ₹100 = ₹8,000. The pump price of ₹94.50 is a trap: it applies only to the first 720 litres, not to the marginal litres. It is also useful to note that the cost of avoiding one litre is ₹100, since that is what the station pays for every litre above the allotment.
2. The SHO proposes to move night beats from jeep B to jeep A until the gap closes. Calculate how many night-beats must be transferred and judge whether the proposal is workable.
Read the worked answer
Fuel per single night-beat
- Jeep B: 120 ÷ 9 = 13.33 L
- Jeep A: 120 ÷ 12 = 10.00 L
- Saving per night transferred: 13.33 − 10.00 = 3.33 L
Nights needed 80 ÷ 3.33 ≈ 24 night-beats - that is, every single night B is currently deployed would have to move to A.
Judgement The arithmetic works exactly (24 × 3.33 = 80 L), but operationally it fails. A already runs 24 nights a month, and taking B's 24 nights as well would give A 48 deployments in a 28–31 day month - roughly 12 nights a week from one vehicle and one driver. No vehicle can be off the road that little and still be serviced, and no driver can be rostered that way. So the proposal closes the gap on paper and breaks the beat plan in practice. A correct answer must therefore reject it on feasibility, not on arithmetic.
3. Using the motorcycle option, find the smallest number of jeep-B nights that must be converted so that consumption stays within 720 litres, and state two operational conditions the SHO must check before adopting the plan.
Read the worked answer
Fuel per motorcycle night-beat 120 km ÷ 35 km/L = 3.43 L, against 13.33 L for jeep B, so each converted night saves 13.33 − 3.43 = 9.90 L.
Minimum number of nights 80 ÷ 9.90 = 8.08, so 8 nights are not enough.
- 8 nights save 79.2 L → total 720.8 L, still over the allotment.
- 9 nights save 89.1 L → total 710.9 L, inside the limit.
Answer: 9 nights (the smallest whole number of nights that actually clears the limit).
Conditions to verify
- The converted stretch must be motorable for a motorcycle - not a muddy or sandy lanka track, especially in the monsoon, and the crew must still be two constables with a working wireless set.
- Vehicle availability, driver licences, helmet and night-visibility rules must be met, and the beat register must show the motorcycle deployment so that the sub-inspector can still prove the beat was covered.
For comparison, converting B nights to jeep A saves only 3.33 L per night and would need 24 nights, confirming the motorcycle is the cheaper fix.