Hostel Mess Purchase Plan
A Sainik School hostel has 240 cadets. The mess has 45 kg of rice and 18 kg of dal in stock. Normal consumption is 150 g of rice and 60 g of dal per cadet per day. After four days, 20 cadets leave for a 10-day national camp, and the rest continue in the hostel. The warden wants to buy enough to last the full 10 days from today, including the four days before the departure. A supplier quotes rice at ₹42 per kg and dal at ₹95 per kg. Orders of 50 kg or more get an 8% discount on the total food value; delivery is free only if the bill before discount is at least ₹3,000, otherwise ₹120 is charged. The warden can buy in whole kilograms only and wants to avoid excess stock by more than 1 kg per item. Prepare a purchase plan.
1. Calculate the quantity of rice and dal that must be purchased. Show the four-day and six-day stages separately.
Read the worked answer
Stage 1: all 240 cadets for 4 days. Rice = 240 × 0.15 × 4 = 144 kg. Dal = 240 × 0.06 × 4 = 57.6 kg.
Stage 2: after 20 leave, 220 cadets remain for 6 days. Rice = 220 × 0.15 × 6 = 198 kg. Dal = 220 × 0.06 × 6 = 79.2 kg.
Total need = 144 + 198 = 342 kg rice; 57.6 + 79.2 = 136.8 kg dal.
Subtract stock: rice 342 − 45 = 297 kg; dal 136.8 − 18 = 118.8 kg.
Whole-kilogram rule: buy 297 kg rice and 119 kg dal. The dal excess is 0.2 kg, within the 1 kg limit.
2. Compute the amount payable to the first supplier and check whether the 8% discount saves more than ₹2,000.
Read the worked answer
Rice cost = 297 × 42 = ₹12,474. Dal cost = 119 × 95 = ₹11,305. Pre-discount total = ₹23,779. Discount = 8% of 23,779 = ₹1,902.32. Payable = 23,779 − 1,902.32 = ₹21,876.68.
The pre-discount bill is above ₹3,000, so delivery is free. The discount is ₹1,902.32, which is less than ₹2,000. The warden's claim that it saves more than ₹2,000 is false.
3. A second supplier offers rice at ₹45 per kg and dal at ₹90 per kg, with no discount but free delivery. Which supplier is cheaper for this purchase plan?
Read the worked answer
Second supplier: rice = 297 × 45 = ₹13,365; dal = 119 × 90 = ₹10,710; total = ₹24,075.
First supplier payable = ₹21,876.68.
Difference = 24,075 − 21,876.68 = ₹2,198.32. The first supplier is cheaper by ₹2,198.32, even though the second has a lower dal price. The 8% discount on the larger combined bill outweighs the dal saving.