Tiered discounts after markup — Radhey Lal marks sweets at 40% above cost. He sells 40% of the stock at the marked price, half of the remaining stock at 14.5% discount on the marked price, and the rest at 25% discount. What is his overall profit.

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Solve this multiple-choice question and choose the correct option.

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Introduction / Context: This is a weighted-average selling price problem: a single markup followed by multiple discount tiers. The overall profit comes from the weighted mean of selling prices versus cost across all items sold. Given Data / Assumptions: Let cost per unit = 100 ⇒ marked price (MP) = 140. 40% sold at MP. From the remaining 60%, 30% (of total) sold at 14.5% discount on MP, and 30% (of total) sold at 25% discount on MP. Concept / Approach: Compute SP for each tranche and take the weighted average SP across 100 units. Overall profit% = (Average SP − Cost)/Cost * 100 with the cost base per unit fixed at 100. Step-by-Step Solution: Tranche A (40 units): SP_A = 140.Tranche B (30 units): SP_B = 140 * (1 − 0.145) = 140 * 0.855 = 119.7.Tranche C (30 units): SP_C = 140 * 0.75 = 105.Average SP = 0.4*140 + 0.3*119.7 + 0.3*105 = 56 + 35.91 + 31.5 = 123.41.Profit% = (123.41 − 100)/100 * 100 = 23.41% ≈ 23.5%. Verification / Alternative check: Total revenue over 100 units = 12,341; total cost = 10,000 ⇒ gain = 2,341 ⇒ 23.41%. Why Other Options Are Wrong: 26.5%, 28.6%, and 30% overstate the weighted effect; 21% understates it. Common Pitfalls: Averaging discount rates instead of revenue, or forgetting to weight by quantities sold at each discount tier. Final Answer: 23.5%

Tiered discounts after markup — Radhey Lal marks sweets at 40% above cost. He sells 40% of the stock at the marked price, half of the remaining stock at 14.5% discount on the marked price, and the rest at 25% discount. What is his overall profit percentage on cost?

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