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?

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:

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%