A man sells two horses for ₹ 1475. The cost price of the first is equal to the selling price of the second. If the first is sold at 20% loss and the second at 25% gain, what is his total gain or loss (in rupees)?

### Concept & Profit/Loss Logic When two items are sold, their overall gain or loss is determined by comparing their total cost price and total selling price. $$ \text{Total Gain/Loss} = \text{Total SP} - \text{Total CP} $$ ### Step-by-Step Solution * Let the Cost Price (CP) of the first horse be $100x$. * The Selling Price (SP) of the second horse equals the CP of the first, so $SP_2 = 100x$. * The first horse is sold at a 20% loss: $SP_1 = 100x - 0.20(100x) = 80x$. * The second horse is sold at a 25% gain, meaning $1.25 \times CP_2 = SP_2 = 100x$. Thus, $CP_2 = \frac{100x}{1.25} = 80x$. * Calculate Total CP = $CP_1 + CP_2 = 100x + 80x = 180x$. * Calculate Total SP = $SP_1 + SP_2 = 80x + 100x = 180x$. * Since Total SP = Total CP, there is no overall gain or loss. (The ₹ 1475 figure is extraneous for the percentage outcome). ### Exam Strategy & Shortcut Always set up variables based on the equating condition. By assuming $CP_1 = SP_2 = 100$, you avoid complex fractions and the extraneous ₹ 1475 value entirely. ### Common Pitfall Trying to use the ₹ 1475 value to find individual prices can lead to messy calculations and wasted time. ### Final Answer Therefore, the correct answer is **Neither gain nor loss**.