A car worth ₹ $1,50,000$ was sold by X to Y at $5\%$ profit. Y sold the car back to X at $2\%$ loss. In the entire transaction (C.P.O., 2007)

### Concept & Net Gain in Circular Transactions When an asset is sold and then bought back by the original owner, the net gain or loss is determined by tracking the net cash flow. The actual cash extracted from the other party defines the net financial profit, given that the asset ends up back where it started. ### Step-by-Step Solution * **Initial State:** X has a car worth ₹ $1,50,000$ and ₹ $0$ in cash. * **First Transaction (X sells to Y):** * X sells at a $5\%$ profit. * Selling Price for X (Cost Price for Y) = $1,50,000 + (5\% \text{ of } 1,50,000) = 1,50,000 + 7,500 = \text{₹ } 1,57,500$. * Now, X has ₹ $1,57,500$ in cash and Y has the car. * **Second Transaction (Y sells back to X):** * Y sells at a $2\%$ loss on his cost price. * Loss for Y = $2\% \text{ of } 1,57,500 = \frac{2}{100} \times 157500 = \text{₹ } 3,150$. * Selling Price for Y (Purchase price for X) = $1,57,500 - 3,150 = \text{₹ } 1,54,350$. * X pays ₹ $1,54,350$ to get the car back. * **Net Result for X:** * X gets his original car back. * Cash remaining with X = $\text{Cash received} - \text{Cash paid} = 1,57,500 - 1,54,350 = \text{₹ } 3,150$. * Since X started with the car and ₹ $0$ cash, and ended with the same car and ₹ $3,150$ cash, X has made a net gain of ₹ $3,150$. ### Exam Strategy & Shortcut Identify the net transfer of cash. Y paid X ₹ $1,57,500$. X paid Y ₹ $1,54,350$. Net cash X extracted from Y = $1,57,500 - 1,54,350 = 3150$. Since X retained the asset in the end, this positive cash flow is pure profit for X. ### Common Pitfall A very common mistake is stating X gained ₹ $7500$ in the first step and lost ₹ $4350$ (difference between $1,54,350$ and intrinsic value of $1,50,000$) in the second. Profit in this closed loop is simply the delta in cash reserves after the asset is retrieved. ### Final Answer Therefore, the correct answer is **X gained ₹ $3150$**.