The Cooperative Store's Two Price Boards
A cooperative store in Nagaon buys 500 kg of rice at ₹40 per kg and pays ₹2,000 in transport. On arrival 20 kg is found damp and unfit for sale. The rest is repacked into 5 kg bags at ₹10 per bag, and only whole bags are sold. The secretary proposes Plan A: sell at ₹54 per kg with no offer. The treasurer proposes Plan B: print ₹58 per kg on the board but give 1 kg free with every 5 kg bought, so a customer who pays for 5 kg carries away 6 kg. A committee member supports Plan B because its printed rate is higher. The store's rule is that no plan may run at a loss, and last monsoon, when stock arrived in the rain, damage touched 60 kg. The committee meets on Friday and wants a decision with figures, not opinions.
1. Work out the profit under Plan A and under Plan B. Which plan should the committee adopt, and why is the higher printed rate misleading?
Read the worked answer
Build the cost first. Purchase: 500 × ₹40 = ₹20,000. Transport: ₹2,000. Saleable stock: 500 − 20 = 480 kg, that is 96 bags, packing 96 × ₹10 = ₹960. Total outlay = ₹22,960.
Plan A: 480 × ₹54 = ₹25,920, so profit = ₹25,920 − ₹22,960 = ₹2,960.
Plan B: each buyer pays for 5 kg and takes 6 kg, so the store receives 58 × 5 = ₹290 per 6 kg unit. Units sold = 480 ÷ 6 = 80. Revenue = 80 × ₹290 = ₹23,200, so profit = ₹240.
Plan B gives up ₹2,720 of margin. The printed rate is not the realised rate: Plan B's effective price is ₹290 ÷ 6 = ₹48.33 per kg, about 16.7% below Plan A's ₹54, even though the board shows ₹58. The member compared two boards instead of two cash flows; the free kilogram is a quantity discount in disguise. Adopt Plan A, or redesign Plan B.
2. A member still wants the '1 kg free' offer because customers respond to it. What printed rate under Plan B would raise exactly the same revenue as Plan A? Show the working and comment on the answer.
Read the worked answer
Plan A raises ₹25,920. Under Plan B that must come from 80 units of 6 kg, so each unit must earn 25,920 ÷ 80 = ₹324.
One unit is 6 kg, of which 5 kg is charged. Printed rate = 324 ÷ 5 = ₹64.80 per kg.
Check: 80 × (₹64.80 × 5) = 80 × ₹324 = ₹25,920. Profit is the same ₹2,960, but the board now reads ₹64.80 against Plan A's ₹54.
The arithmetic is honest but the design is poor. To match Plan A the store must display a price 20% above its competitor-facing rate, which invites the very comparison the offer was meant to avoid, and it depends on customers not dividing by six. If the committee rounds to ₹65, revenue becomes 80 × ₹325 = ₹26,000, a profit of ₹3,040 - only ₹80 better than Plan A while carrying higher pricing risk. The simpler recommendation stands: a plain per-kilogram rate is easier to defend and to audit.
3. In a bad monsoon, damage rises to 60 kg. What is the minimum Plan A price that avoids a loss, and what does the comparison with the 20 kg case tell the committee about procurement?
Read the worked answer
Recalculate from scratch, because packing cost changes with bag count. Saleable stock = 500 − 60 = 440 kg = 88 bags; packing = 88 × ₹10 = ₹880. Outlay = ₹20,000 + ₹2,000 + ₹880 = ₹22,880.
Break-even price = 22,880 ÷ 440 = ₹52.00 per kg exactly. Any price above ₹52 clears the no-loss rule; at ₹54 the profit is 440 × 54 = ₹23,760 − ₹22,880 = ₹4,880.
The instructive part is the size of the swing. Going from 20 kg to 60 kg of damage removes 40 kg of sellable rice, worth 40 × ₹54 = ₹2,160 of revenue, besides the ₹1,600 already paid for it - roughly ₹3,760 wiped off a ₹2,960 margin. The margin is thinner than the damage risk. The committee should therefore spend on covered transport or on-the-spot weighing before it spends on advertising, and should treat ₹52 as the floor below which a damaged consignment must be renegotiated with the supplier rather than absorbed.