A bought a radio set and spent ₹ $110$ on its repairs. He then sold it to B at $20\%$ profit, B sold it to C at a loss of $10\%$ and C sold it for ₹ $1188$ at a profit of $10\%$. What is the amount for which A bought the radio set?

### Concept & Reverse Supply Chain Tracking When the final selling price is given at the end of a chain of transactions, we calculate backwards to find the initial cost price. Additionally, any overhead expenses (like repairs) must be factored into the original purchaser's total cost price before applying profit percentages. ### Step-by-Step Solution Let's track the prices backwards from C to A. * **C's Transaction:** C sold it for ₹ $1188$ at a $10\%$ profit. * Let C's Cost Price be $CP_c$. * $CP_c \times (1 + 0.10) = 1188$ * $1.10 \times CP_c = 1188 \implies CP_c = \frac{1188}{1.1} = \text{₹ } 1080$. * **B's Transaction:** B sold it to C at a $10\%$ loss. B's Selling Price is C's Cost Price (₹ $1080$). * Let B's Cost Price be $CP_b$. * $CP_b \times (1 - 0.10) = 1080$ * $0.90 \times CP_b = 1080 \implies CP_b = \frac{1080}{0.9} = \text{₹ } 1200$. * **A's Transaction:** A sold it to B at a $20\%$ profit. A's Selling Price is B's Cost Price (₹ $1200$). * Let A's *Total* Cost Price be $CP_a$. * $CP_a \times (1 + 0.20) = 1200$ * $1.20 \times CP_a = 1200 \implies CP_a = \frac{1200}{1.2} = \text{₹ } 1000$. * A's total cost includes the purchase price plus the repair costs. * $\text{Purchase Price} + \text{Repairs} = 1000$ * $\text{Purchase Price} + 110 = 1000$ * $\text{Purchase Price} = 1000 - 110 = \text{₹ } 890$. ### Exam Strategy & Shortcut Chain the multipliers in a single equation. Let the initial purchase price be $x$. Total initial cost = $(x + 110)$. Chain: $(x + 110) \times 1.2 \times 0.9 \times 1.1 = 1188$ $(x + 110) \times 1.188 = 1188$ $(x + 110) = 1000$ $x = 890$. ### Common Pitfall A frequent mistake is applying the repair cost of ₹ $110$ to the end of the calculation rather than incorporating it into A's baseline cost price before calculating A's $20\%$ profit. ### Final Answer Therefore, the correct answer is **₹ $890$**.