Profits - Maximum
- 2. Profit & Loss A merchant buys 80 articles, each at Rs. 40. He sells n of them at a profit of n% and the remaining at a profit of (100 – n)%. What is the minimum profit the merchant could have made on this trade? (a) Rs. 2160 (b) Rs. 1420 (c) Rs. 1580 (d) Rs. 2210
- 3. Profit & Loss CP = 80 × 40 Profit from the n objects = n% × 40 × n. Profit from the remaining objects = (100 – n)% × 40 × (80 – n). A merchant buys 80 articles, each at Rs. 40. He sells n of them at a profit of n% and the remaining at a profit of (100 – n)%. What is the minimum profit the merchant could have made on this trade?
- 4. Profit & Loss We need to find the minimum possible value of n% × 40 × n + (100 – n)% × 40 × (80 – n). Or, we need to find the minimum possible value of n2 + (100 – n) (80 – n). Minimum of n2 + n2 – 180n + 8000 Minimum of n2 – 90n + 4000 Minimum of n2 – 90n + 2025 – 2025 + 4000 A merchant buys 80 articles, each at Rs. 40. He sells n of them at a profit of n% and the remaining at a profit of (100 – n)%. What is the minimum profit the merchant could have made on this trade?
- 5. Profit & Loss We add and subtract 2025 to this expression in order to crate an expression that can be expressed as a perfect square. This approach is termed as the “Completion of Squares” approach. We keep revisiting this in multiple chapters. Minimum of n2 – 90n + 2025 + 1975 = (n – 45)2 + 1975 This reaches minimum when n = 45. A merchant buys 80 articles, each at Rs. 40. He sells n of them at a profit of n% and the remaining at a profit of (100 – n)%. What is the minimum profit the merchant could have made on this trade?
- 6. Profit & Loss When n = 45, the minimum profit made 45% × 40 × 45 + 55% × 40 × 35 18 × 45 + 22 × 35 = 810 + 770 Rs. 1580 Answer choice (c) A merchant buys 80 articles, each at Rs. 40. He sells n of them at a profit of n% and the remaining at a profit of (100 – n)%. What is the minimum profit the merchant could have made on this trade?
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