Two Tankers, Ten Hours, Eighteen Thousand People
You are in charge of emergency water supply for a tehsil during a ten-day drought. Three union councils need drinking water: UC-A has 9,000 residents, UC-B 6,000 and UC-C 3,000. The standard agreed with the district office is 5 litres per person per day. You have one government tanker of 10,000 litres. A full round trip - filling at the tube well, driving to the councils, discharging - takes 2 hours. Operation is permitted only between 06:00 and 16:00, because of the tube well's power schedule. A transport contractor offers one hired tanker of 6,000 litres whose round trip takes 2.5 hours; he will run it only inside the same ten-hour window. No union council has a storage tank, so water delivered today is drunk today and nothing carries over. The district office wants a one-page supply plan by noon. UC-C's councillor has already threatened a protest, on the ground that his council is the smallest and is usually served last.
1. Task 1. Calculate the maximum volume you can deliver in one day and the shortfall against the agreed standard. Show every step, and state which of your figures are ceilings rather than forecasts.
Read the worked answer
Government tanker: 10-hour window ÷ 2-hour round trip = 5 trips. 5 × 10,000 L = 50,000 L.
Hired tanker: 10 ÷ 2.5 = 4 trips exactly. 4 × 6,000 L = 24,000 L.
Combined maximum: 74,000 L per day.
Requirement: 9,000 + 6,000 + 3,000 = 18,000 people × 5 L = 90,000 L.
Shortfall: 16,000 L per day, about 17.8% of requirement. Per person, 74,000 ÷ 18,000 = 4.11 L.
Two cautions belong in the same page of the plan. First, both trip counts assume no queueing at the tube well, no breakdown and no driver break; the real figure will be lower, so 74,000 L is a ceiling, not a forecast. Second, because nothing is stored, a trip lost at 15:00 cannot be recovered tomorrow - the shortfall is permanent for that day. A prudent planning figure is 68,000–72,000 L, and the allocation should be built on that, not on the ceiling.
2. Task 2. Propose tomorrow's allocation across the three union councils and defend it against the councillor's complaint. Your answer must state the volume and the litres per head for each council.
Read the worked answer
Proposal: universal rationing at 4 L per head - UC-A 36,000 L, UC-B 24,000 L, UC-C 12,000 L = 72,000 L - leaving 2,000 L in reserve for the two clinics, the shelter school and a lost-trip contingency. Within each council, tanker points are announced one day in advance and served in rotation, so no street is permanently last.
Why not 5 L for a protected group first? It looks more humane but it is not deliverable: protecting 5 L for the roughly 3,000 children under five and pregnant women consumes the whole 15,000 L gap and leaves 3.5 L for everyone else, which is harder to explain than a flat 4 L.
Answer to the councillor: UC-C already receives its full per-head share - 12,000 L against a population of 3,000 - and its share is not reduced by its size. In addition, UC-C gets the first slot on alternate days, so if a trip is lost it is lost by the larger councils, not his. Put this in writing before the protest, not after it.
3. Task 3. The district office asks for one operational change that would close the gap. Identify it, calculate its effect, and state the assumptions on which it depends.
Read the worked answer
The change: extend the operating window by 2.5 hours, to 18:30.
The two tankers respond differently, and this is where most answers go wrong.
- Government tanker: 12.5 ÷ 2 = 6 trips, i.e. +1 trip = +10,000 L.
- Hired tanker: 12.5 ÷ 2.5 = 5 trips, i.e. +1 trip = +6,000 L.
- New total 74,000 + 16,000 = 90,000 L, exactly the requirement.
A 2-hour extension would give the big tanker its extra trip but leave the hired tanker on four trips, because 12 hours holds only four complete 2.5-hour round trips. The extension must therefore be sized to the slower vehicle.
Assumptions to verify before signing: the tube well has power and water after 16:00 (the stated reason for the window); the contractor's driver and the escort accept evening duty; and the councils can receive and distribute after dark. Note also that a plan delivering exactly 90,000 L has no margin - one breakdown restores the shortfall, so keep the 2,000 L reserve or add a second hired tanker.