Shortcut Trick
Total items are divided into 3 parts (since 1/3 is sold first).
Let the total quantity be 3 units. 1 unit is sold at 15% loss (−15).
Remaining 2 units must be sold at x% profit (+x).
Total target profit is 20% on 3 units: 3 × 20 = 60.
Equation: 1 × (−15) + 2 × x = 60 ⇒ 2x = 60 + 15 = 75 ⇒ x = 37.5%.
∴ The correct answer is 37.5%.
Alternate Method
Given: Total CP = Rs 4,500, Total Profit = 20%, Loss on 1/3 = 15%.
Formulas: Profit = SP − CP | SP = CP × (100 + P%)/100 | Total Profit = (P1 + P2 + ...)
⇒ Total required SP = 4500 × (120/100) = Rs 5,400.
⇒ CP of 1/3 articles = 4500 ÷ 3 = Rs 1,500.
⇒ SP of 1/3 articles = 1500 × (85/100) = Rs 1,275.
⇒ Remaining CP = 4500 − 1500 = Rs 3,000.
⇒ Required SP of remaining = 5400 − 1275 = Rs 4,125.
⇒ Profit needed = 4125 − 3000 = Rs 1,125.
⇒ Profit% = (1125 ÷ 3000) × 100 = 37.5%.
∴ The correct answer is 37.5%.
Additional Information
Weighted Average Method
When parts of goods are sold at different profit/loss rates, the overall profit/loss is the weighted average: Total% = (n1p1 + n2p2) / (n1 + n2).
Independence from Absolute Value
In percentage-based profit/loss questions involving parts of a whole, the actual Cost Price (Rs 4,500) does not affect the final percentage result and can be ignored for faster calculation.