An avionics vendor marks up the price of a navigation sensor by $40\%$ above its manufacturing cost price. During a procurement discount drive, the vendor offers a cash discount of $15\%$ on the marked price. What is the vendor's net percentage profit on the sale?

Answer Key:

19.0

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Base Assumption:** Let the Cost Price ($CP$) = ₹100. 2. **Stage 2: Marked Price ($MP$):** Marked up by $40\% \implies MP = 100 \times 1.40 = 140$. 3. **Stage 3: Selling Price ($SP$) after Discount:** * Discount of $15\%$ on $MP$: * $SP = 140 \times (1 - 0.15) = 140 \times 0.85 = 119$. 4. **Stage 4: Profit Percentage:** * $\text{Profit} = SP - CP = 119 - 100 = 19$. * $\text{Profit \%} = \frac{19}{100} \times 100\% = 19.0\%$. 5. **Stage 5: Alternative Successive Formula:** Net $\% = x + y + \frac{xy}{100} = +40 - 15 - \frac{40 \times 15}{100} = 25 - 6 = 19\%$.

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