A man purchases two clocks A and B at a total cost of ₹ 650. He sells A with 20% profit and B at a loss of 25% and gets the same selling price for both the clocks. What are the purchasing prices of A and B respectively?

### Concept & Equating Selling Prices When selling prices are equal but profit/loss percentages differ, setting up a ratio between the cost prices simplifies the problem significantly. $$ SP = CP \times (1 \pm \text{Profit/Loss} \%) $$ ### Step-by-Step Solution * Let the Cost Price of clock A be $CP_A$ and clock B be $CP_B$. * Total cost: $CP_A + CP_B = 650$. * Clock A is sold at a 20% profit: $SP_A = 1.20 \times CP_A$. * Clock B is sold at a 25% loss: $SP_B = 0.75 \times CP_B$. * Given that selling prices are equal: $1.20 \times CP_A = 0.75 \times CP_B$. * Multiply both sides by 100 to remove decimals: $120 \times CP_A = 75 \times CP_B$. * Divide by 15: $8 \times CP_A = 5 \times CP_B$. * Thus, the ratio of their cost prices is $CP_A : CP_B = 5 : 8$. * The total parts in the ratio are $5 + 8 = 13$ parts, equivalent to ₹ 650. * One part is $\frac{650}{13} = 50$. * $CP_A = 5 \times 50 = 250$. * $CP_B = 8 \times 50 = 400$. ### Exam Strategy & Shortcut If $SP_1 = SP_2$, then $CP_1 \times (100 + P\%) = CP_2 \times (100 - L\%)$. So $CP_1 / CP_2 = 75 / 120 = 5 / 8$. Distribute 650 in the ratio 5:8 immediately to get 250 and 400. This avoids all complex algebra. ### Common Pitfall Confusing the profit/loss multipliers (e.g., using 0.80 instead of 1.20, or setting the ratio as 8:5 instead of 5:8). ### Final Answer Therefore, the correct answer is **₹ 250, ₹ 400**.