A company offers three types of successive discounts (i) 25% and 15% ; (ii) 30% and 10% ; (iii) 35% and 5%. Which offer is the best for a customer? (S.S.C., 2007)

### Concept & Equivalent Discount Maximization For any two successive discounts $a\%$ and $b\%$, the single equivalent discount is: $$Equivalent Discount = a + b - \frac{a \times b}{100}$$ For a customer, the "best" offer is the one that gives the highest total discount. If the sum $(a+b)$ is constant across options, the maximum discount is obtained when the product $(a \times b)$ is minimized. ### Step-by-Step Solution * **Check the sum of discounts for all offers:** * (i) $25 + 15 = 40$ * (ii) $30 + 10 = 40$ * (iii) $35 + 5 = 40$ * Since the sum is $40$ in all cases, the equivalent discount will be $40 - \frac{ab}{100}$. * **Evaluate the product $ab$ for each offer:** * (i) $25 \times 15 = 375$ * (ii) $30 \times 10 = 300$ * (iii) $35 \times 5 = 175$ * **Determine the best offer:** * The offer with the smallest product will subtract the least amount from $40$, yielding the highest net discount. * Since $175$ is the smallest product, offer (iii) yields the highest discount ($40 - 1.75 = 38.25\%$). ### Exam Strategy & Shortcut Whenever a set of successive discounts has the same arithmetic sum, the combination with the **greatest difference** between the two percentage values always gives the maximum total discount. Between $(25, 15)$, $(30, 10)$, and $(35, 5)$, the gap is largest for $35\%$ and $5\%$, making it instantly recognizable as the best offer for a buyer. ### Common Pitfall A common mistake is choosing "All are equally good" because the sums ($25+15$, $30+10$, $35+5$) all equal $40\%$. The base for the second discount changes, which fundamentally alters the total discount amount. ### Final Answer Therefore, the correct answer is **Third offer**.