Ronit and Vinit purchased a scooter for ₹ 25000 and sold the same for ₹ 26250. If at the time of purchase Ronit paid $1 \frac{1}{2}$ times as much as Vinit, how much did Vinit receive out of profit? (P.C.S., 2004)

### Concept & Profit Sharing Ratio When multiple partners invest in a single asset, the absolute profit earned is distributed among them in the exact ratio of their initial investments. ### Step-by-Step Solution * **Determine Total Profit:** * Total Cost Price (CP) = ₹ 25000 * Total Selling Price (SP) = ₹ 26250 * Total Profit = $26250 - 25000 = 1250$ rupees. * **Establish Investment Ratio:** * Let Vinit's investment be $x$. * Ronit paid $1 \frac{1}{2}$ times as much, so Ronit's investment = $1.5x = \frac{3}{2}x$. * Ratio of investment (Ronit : Vinit) = $\frac{3}{2}x : x = 3 : 2$. * **Calculate Individual Profit Share:** * The profit must be divided into $3 + 2 = 5$ equal parts. * Vinit's share corresponds to $2$ parts out of $5$. * Vinit's profit = $\frac{2}{5} \times \text{Total Profit} = \frac{2}{5} \times 1250$. * Vinit's profit = $2 \times 250 = 500$ rupees. ### Exam Strategy & Shortcut Quickly find the ratio $1.5 : 1$ which is $3 : 2$. This means Vinit gets $\frac{2}{5}$ of the total pie. The total profit is simply $26250 - 25000 = 1250$. Mentally calculate $\frac{2}{5}$ of $1250 = 500$. You don't need to calculate their exact individual contribution amounts. ### Common Pitfall A common mistake is trying to figure out the exact rupee amount each person paid initially (15000 and 10000). While correct, it adds unnecessary calculation steps and wastes precious exam time. ### Final Answer Therefore, the correct answer is **₹ 500**.