Flour Stock and the Day-35 Convoy
Your company of 480 cadets is drawing flour from a store holding 36 days' ration at 750 g per cadet per day. On day 12, 80 cadets are transferred to another wing and the medical officer orders the per-head ration cut to 600 g. The storekeeper, working from memory, tells the quartermaster the remaining stock will last 'about 30 more days' and recommends the resupply convoy be brought forward. The quartermaster must approve or reject that recommendation before the convoy sails on day 35, counted from day 1 of the ration cycle. No wastage allowance has been applied to any of these figures, and the store has a history of about 4 per cent loss to spillage, damp and scoop shortfall. The storekeeper is popular and has 19 years' service; the quartermaster has asked you, a cadet clerk, to check the arithmetic before he signs.
1. Calculate how long the remaining stock actually lasts from day 12, and state whether the storekeeper's 30-day claim is correct.
Read the worked answer
Work in kilograms throughout.
Step 1 - initial holding. 480 cadets × 0.75 kg × 36 days = 12,960 kg.
Step 2 - consumed by end of day 12. 480 × 0.75 × 12 = 4,320 kg.
Step 3 - remaining at day 12. 12,960 − 4,320 = 8,640 kg.
Step 4 - new daily draw. (480 − 80) = 400 cadets × 0.60 kg = 240 kg/day.
Step 5 - duration. 8,640 ÷ 240 = 36 days, i.e. stock reaches day 48 (12 + 36).
Verdict: the claim is wrong in the safe direction - it understates endurance by 6 days. The error comes from applying the new 600 g rate to a stock figure that was built on 750 g, and from rounding 'about 30'. It is a memory estimate, not a calculation, and it should not be signed as one.
2. On day 25, 60 extra cadets arrive and the ration is restored to 700 g. Recalculate when the stock runs out, and say whether the day-35 convoy is still adequate.
Read the worked answer
Segment 1 - day 12 to day 25 (13 days at the old rate). 240 kg/day × 13 = 3,120 kg. Remaining: 8,640 − 3,120 = 5,520 kg.
Segment 2 - from day 25. Strength: 400 + 60 = 460 cadets. Rate: 460 × 0.70 = 322 kg/day.
Duration: 5,520 ÷ 322 = 17.1 days, so the store empties around midday on day 42 (25 + 17.1).
Adequacy: the convoy arrives on day 35, leaving roughly 7 days of cover - adequate, but thinner than the 13 days that existed before the reinforcement and the ration restoration. Note the sensitivity: the answer moves by almost a full day for every 20 cadets added at this stage, because the daily draw is now 322 kg against a stock of only 5.5 tonnes.
3. The quartermaster asks whether the storekeeper's 30-day figure should be used as the planning figure for the convoy. Give your recommendation with reasoning.
Read the worked answer
Recommendation: reject 30 days and plan on 36 days, less a wastage allowance - but do not sail the convoy early on the strength of it.
Reasoning:
- Correct the arithmetic first. 36 days is reproducible and auditable; 30 days is a recollection. A planning figure that cannot be shown on paper should never be signed.
- Apply the 4 per cent loss. Effective stock ≈ 8,640 × 0.96 = 8,294 kg, giving about 34.5 days rather than 36. That is the honest endurance - still far beyond day 35.
- Check the direction of the error. The storekeeper's mistake is conservative (it shortens endurance), so it does not endanger the troops; it merely wastes money by moving a convoy earlier than needed. That distinction matters when you write the note: it is an accuracy problem, not a negligence problem.
- Say what would change the answer. Arrival of formed bodies, a further ration change, or a failed convoy would all compress the margin; recommend a recheck at day 28 rather than a single forecast made on day 12.