Two Vehicles, One Fuel Ceiling: Posting Kilometres on a Fixed Budget
A sub-divisional police office in Odisha runs two diesel patrol vehicles. The older vehicle, A, gives 12 km per litre; the newer vehicle, B, gives 14 km per litre. Diesel costs Rs 90.00 per litre and the office's monthly fuel ceiling is Rs 25,000. The patrol requirement is 3,600 km a month, spread over 26 patrolling days. At present every kilometre is logged on A, because B is treated as the officer's vehicle and stays parked unless the SDPO travels. The accountant reports that the fuel bill has crossed the ceiling for three months, and the treasury has asked for a written explanation and a recovery plan. B is also due for servicing for three days every month, and on those days it cannot be used at all. The SDPO wants a one-page note that keeps patrol running at 3,600 km and stays inside Rs 25,000.
1. Compute the present monthly fuel cost and state the shortfall against the ceiling.
Read the worked answer
Present practice means all 3,600 km on vehicle A at 12 km per litre.
- Litres: 3,600 / 12 = 300 litres.
- Cost: 300 x Rs 90 = Rs 27,000.
- Ceiling: Rs 25,000. Excess: Rs 2,000, i.e. 8 per cent over.
Useful supporting figures for the note:
- Budget in litres: 25,000 / 90 = 277.78 litres.
- Per patrolling day: 3,600 / 26 = 138.5 km, costing Rs 1,038 a day on A.
The diagnosis is not that patrol is excessive but that the more efficient vehicle is idle. The note should say so explicitly, because a recovery plan that simply cuts kilometres would reduce visible patrol, which is the wrong saving.
2. Find the maximum distance that can be run on the older vehicle each month while staying within Rs 25,000, and set out a practical posting plan.
Read the worked answer
Let x km be run on A and (3,600 - x) km on B.
Litres = x/12 + (3,600 - x)/14 = [14x + 12(3,600 - x)] / 168 = (2x + 43,200) / 168
Set this at or below 277.78 litres: 2x + 43,200 is at most 46,667 2x is at most 3,467 x is at most 1,733 km
So A may run roughly 1,733 km a month and B must take at least 1,867 km. Check: 1,733/12 = 144.4 litres plus 1,867/14 = 133.4 litres, total 277.8 litres, Rs 25,000.
Practical posting: A takes short urban beats and station-linked work, about 65 km a day for 26 days; B takes highway and night-highway patrol. Note the temptation to shift everything to B: all-B costs 257.1 litres, Rs 23,143, which looks better but leaves no reserve for B's servicing days and forces A back into use without a planned limit. The plan should state the 1,733 km cap on A as a monthly figure to be checked weekly.
3. B is off the road for three days each month for servicing, and those days must be covered by A. Does the plan still fit the budget? Show the arithmetic.
Read the worked answer
Daily requirement: 3,600 / 26 = 138.5 km. Over the three servicing days, A must do 3 x 138.5 = 415.4 km.
- Servicing-window fuel: 415.4 / 12 = 34.6 litres, i.e. Rs 3,115.
- Remaining distance: 3,600 - 415.4 = 3,184.6 km.
- Remaining budget: Rs 25,000 - Rs 3,115 = Rs 21,885, which is 243.2 litres.
- Those 3,184.6 km on B need 3,184.6 / 14 = 227.5 litres, costing Rs 20,472.
- Total: 34.6 + 227.5 = 262.1 litres, Rs 23,587 - about Rs 1,413 inside the ceiling.
So it fits, but only if the 415 km done in the servicing window is counted inside A's 1,733 km cap, leaving about 1,318 km for the rest of the month on A. Otherwise A is over-posted by roughly 415 km and the overspend returns.
Sensitivity worth stating in the note: total consumption is 262.1 litres, so the plan holds up to a diesel price of about Rs 95 a litre; beyond that the kilometres must be re-posted, not the ceiling exceeded.