Fuel Quota for Three Night Beats
A district police control room in Bihar must plan fuel for three fixed night-patrol beats over a 30-day month beginning 1 September. Beat 1 is 90 km per night, Beat 2 is 60 km and Beat 3 is 45 km. Three jeeps are available. Jeep A gives 15 km per litre of petrol, Jeep B gives 10 km/l and Jeep C gives 18 km/l; all three draw from the same depot and the depot issues fuel only against a monthly quota of 400 litres. The transport officer's standing rule is that the most fuel-efficient available jeep must be placed on the longest beat every night, and no jeep may run two beats on the same night. From 10 to 15 September, six nights, Jeep C is at the district workshop for engine repair and is not available. The control room must also keep a 10 per cent reserve of the month's quota untouched for emergencies, and the reserve cannot be spent without the SP's written sanction.
1. Calculate the month's fuel consumption if the standing rule is followed, and state whether the 400-litre quota holds without touching the reserve.
Read the worked answer
Step 1 - the best assignment on a normal night. Jeep C (18 km/l) on the 90-km beat = 90 ÷ 18 = 5.0 L. Jeep A (15 km/l) on the 60-km beat = 60 ÷ 15 = 4.0 L. Jeep B (10 km/l) on the 45-km beat = 45 ÷ 10 = 4.5 L. Total = 13.5 L per night.
Step 2 - normal nights. September has 9 nights before the repair (1–9) and 15 nights after it (16–30), i.e. 24 normal nights. 24 × 13.5 = 324 L.
Step 3 - the six repair nights. Only A and B are available for three beats, so the 'no jeep runs two beats' rule must be broken. Compare the options by total litres: A on 90 + 45 = 135 km ÷ 15 = 9.0 L and B on 60 ÷ 10 = 6.0 L gives 15.0 L; A on 90 = 6.0 L and B on 60 + 45 = 105 ÷ 10 = 10.5 L gives 16.5 L; A on 105 = 7.0 L and B on 90 = 9.0 L gives 16.0 L. The cheapest is 15.0 L per night, so 6 × 15.0 = 90 L.
Step 4 - month total = 324 + 90 = 414 L against a 400-litre quota. The quota is exceeded by 14 L, and the 40-litre reserve is inside that quota, so the answer is: not sufficient.
2. During the six repair nights, which jeep should take the 45-km beat, and what does that decision cost over leaving the beat uncovered?
Read the worked answer
The 45-km beat cannot be left uncovered - an uncovered beat is an operational failure, not a saving - so it must be attached to one of the two working jeeps. The arithmetic favours attaching it to Jeep A: A covers 90 + 45 = 135 km at 15 km/l = 9.0 L while B covers 60 km at 10 km/l = 6.0 L, a nightly total of 15.0 L. The reverse arrangement, B covering 105 km at 10 km/l = 10.5 L, costs 1.5 L more each night, or 9 L over the six nights, because B is the least efficient vehicle and should be given the shortest distance. Attaching the 45-km beat to A therefore costs 15.0 − 13.5 = 1.5 L extra per night against the normal-night figure, i.e. 9 L over the repair period. That 9 L is the real price of the workshop visit; it is small and should be reported as a planned deviation rather than hidden by dropping the beat.
3. The SP refuses extra fuel. Recommend one change, with numbers, that keeps all three beats running every night and keeps the reserve intact.
Read the worked answer
Merge Beat 1 and Beat 3 into a single run for Jeep C, since the two routes share a stretch and the clubbing adds little distance beyond the 135 km already counted. Every night: C covers 135 km at 18 km/l = 7.5 L, A covers 60 km at 15 km/l = 4.0 L, total 11.5 L instead of 13.5 L - a saving of 2.0 L per night.
Full month with the repair period still included: 24 normal nights × 11.5 = 276 L; six repair nights with A covering 135 km (9.0 L) and B covering 60 km (6.0 L) = 15.0 L × 6 = 90 L. Total = 366 L against a 400-litre quota, leaving 34 L spare and the 40-litre reserve untouched.
The judgment being tested is that the standing rule ('most efficient jeep on the longest beat') is a means, not an end. Re-cutting the beat boundaries saves more fuel than any jeep swap, and it does so without cancelling a beat, breaching the reserve, or asking for a sanction the SP has already refused.