Blended rice, short weights and the true margin
A wholesale grocer buys 100 kg of rice variety X at Rs. 150 per kg and 150 kg of variety Y at Rs. 200 per kg, and sells the two only as a blend. The blended stock is offered at Rs. 216 per kg, which the grocer describes to customers as '20% above cost'. At the counter, staff use a 900-gramme weight in place of the one-kilogramme weight when weighing out every sale; the same 900-gramme weight is used for all customers and for all quantities, and there is no other irregularity. There is no wastage, no moisture loss, and the entire 250 kg is sold within the month. The owner has asked the accountant to review the month's results and to confirm whether the '20% above cost' description, and the margin actually earned, are consistent with each other. Sales are all cash and there are no other costs to consider.
1. Compute the total cost of the blended stock, the total revenue actually collected, and the realised profit as a percentage of cost.
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Cost: (100 × 150) + (150 × 200) = 15,000 + 30,000 = Rs. 45,000 for 250 kg, i.e. Rs. 180 per kg weighted average.
Quantity charged to customers: because each 'kg' handed over is really 0.9 kg, 250 real kg is billed as 250 / 0.9 = 277.78 kg.
Revenue: 277.78 × 216 = Rs. 60,000. (Check: 250 × 216 / 0.9 = 60,000.)
Profit: 60,000 − 45,000 = Rs. 15,000, which is 15,000 / 45,000 = 33.33% of cost.
Shorter route: 216 / 180 = 1.20 gives the 20% uplift, and the short weight multiplies revenue by 1/0.9 = 1.1111, so the realised margin is 1.20 / 0.90 − 1 = 33.33%. The short weight is worth 13.33 percentage points of margin - more than the entire stated mark-up.
2. Explain why the realised margin differs from the claimed 20% and identify the single adjustment figure that reconciles the two.
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The 20% claim is a pure price-over-cost statement: Rs. 216 against Rs. 180 per kg. It would be correct only if each customer received a full kilogramme per kilogramme charged. The 900-gramme weight means the 20% price uplift is applied to a quantity that is 11.11% smaller than the quantity paid for, so the two effects compound rather than add.
Reconciling factor: revenue is inflated by 1/0.9 = 1.1111 on every rupee of list price. Applying that to the 20% uplift gives 1.20 × 1.1111 = 1.3333, i.e. 33.33% on cost.
The claim is therefore not merely optimistic, it is misleading in a way that is legally exposed: short weight on a stated measure is a weights-and-measures offence in most jurisdictions, independent of whether the price per stated kilogramme is itself reasonable. The accountant's note should separate the pricing question (20% mark-up, defensible) from the measurement question (900 g sold as 1 kg, not defensible) and should not blend them into one margin figure.
3. An inspector orders the grocer to use correct weights, and the owner separately decides to give a 5% trade discount off the Rs. 216 list price. What list price per kg must the grocer now set to keep the same total rupee profit of Rs. 15,000 on 250 kg?
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With honest weights, the grocer sells exactly 250 kg, so the required profit per kg is 15,000 / 250 = Rs. 60.
Required net selling price = cost per kg + 60 = 180 + 60 = Rs. 240 per kg.
That Rs. 240 is the price after the 5% discount. Let the marked price be M:
0.95M = 240 → M = 240 / 0.95 = Rs. 252.63 per kg (to the nearest paisa).
Check: 250 × 252.63 = 63,157.50 gross; less 5% = 59,999.63, i.e. Rs. 60,000 revenue; less Rs. 45,000 cost = Rs. 15,000 profit.
The judgement point is that the grocer cannot simply add the 5% discount back onto Rs. 240; the discount is calculated on the marked price, so it must be grossed up by dividing by 0.95, not multiplied by 1.05. Marking at 240 × 1.05 = Rs. 252 would leave only Rs. 239.40 net and fail the target by Rs. 150 overall.