Fuel Allotment, Patrol Routes and a Festival Order
Assume you are the constable in charge of transport at a rural police station. The station has 2 jeeps and 3 motorcycles. Each jeep is required to cover 56 km a day on patrol, and each motorcycle 42 km a day. A jeep runs 7 km per litre of diesel; a motorcycle runs 28 km per litre of petrol. The station receives a monthly allotment of 450 litres of diesel and 120 litres of petrol, and for this purpose the month is treated as 30 days. Fuel is drawn at the start of the month. On the 18th, the Officer-in-Charge orders that for the last five days of the month each jeep must add a 12 km daily trip to a ferry ghat because of a festival. No extra allotment is available. Diesel from the emergency fund costs ₹90 a litre and petrol ₹105 a litre. The IC asks you to work out the fuel position before the festival order.
1. Calculate the station's monthly diesel and petrol requirement under the normal patrol plan and state the shortfall against the allotment.
Read the worked answer
Diesel: 2 jeeps × 56 km = 112 km/day; at 7 km/L this is 16 L/day; for 30 days, 480 L. The allotment is 450 L, so the shortfall is 30 L. Petrol: 3 motorcycles × 42 km = 126 km/day; at 28 km/L this is 4.5 L/day; for 30 days, 135 L. The allotment is 120 L, so the shortfall is 15 L. The normal plan therefore requires 480 L of diesel and 135 L of petrol, and the station is short by 30 L and 15 L respectively before any festival duty is added.
2. The IC will not buy fuel. Find the equal daily reduction per jeep that makes the diesel allotment last exactly 30 days, and state the effect on patrol coverage.
Read the worked answer
To save 30 L over 30 days, diesel use must fall by 1 L/day. At 7 km/L, 1 L supports 7 km, so the two jeeps together must cut 7 km/day, which is 3.5 km per jeep per day. Each jeep would run 52.5 km/day instead of 56 km/day. Check: 2 × 52.5 = 105 km/day; 105 ÷ 7 = 15 L/day; 15 × 30 = 450 L, exactly the allotment. This closes the diesel gap, but it reduces total jeep patrol coverage by 7 km/day. The petrol shortfall is unaffected by this measure and still requires a separate decision.
3. If the reduction from the previous task has been in force since day 1, what is the diesel overrun caused by the festival order, and what is the emergency-fund cost at ₹90 a litre?
Read the worked answer
Festival extra distance: 2 jeeps × 12 km × 5 days = 120 km. At 7 km/L this is 120 ÷ 7 = 17.14 L. With the 3.5 km per jeep cut in force from day 1, ordinary diesel use is 450 L, so the station would need 450 + 17.14 = 467.14 L, which is 17.14 L over the allotment. Emergency diesel cost = 17.14 × ₹90 = ₹1,542.86, approximately ₹1,543. The plan is therefore not fully within allotment; the IC must either extend the route cut over the last five days or buy the extra fuel.