Dhar bought two articles A and B at a total cost of ₹ 8000. He sold article A at 20% profit and article B at 12% loss. In the whole deal he made no gain and no loss. At what price should Dhar have sold article B to make an overall profit of 25%?

### Concept & Formula The net gain or loss being zero means the profit on one article exactly offsets the loss on the other. Overall profit requirement is based on the total cost price of both articles. ### Step-by-Step Solution 1. **Find CP of each article:** Let the cost price of article A be $x$ and article B be $8000 - x$. Profit on A = $20\%$ of $x = 0.2x$ Loss on B = $12\%$ of $(8000 - x) = 0.12(8000 - x)$ Since there is no net gain or loss: $$0.2x = 0.12(8000 - x)$$ $$0.2x = 960 - 0.12x$$ $$0.32x = 960$$ $$x = \frac{960}{0.32} = 3000$$ So, CP of A = ₹ 3000, and CP of B = ₹ 5000. 2. **Calculate required SP of B:** To make an overall profit of $25\%$ on the total cost (₹ 8000): Total Target SP = $8000 \times 1.25 =$ ₹ 10000 Actual SP of A (sold at $20\%$ profit) = $3000 \times 1.20 =$ ₹ 3600 Required SP of B = Total Target SP - SP of A Required SP of B = $10000 - 3600 =$ ₹ 6400 ### Exam Strategy & Shortcut Instead of solving for $x$, use the method of Alligation to find the ratio of their Cost Prices directly: Profit on A = $+20\%$ Loss on B = $-12\%$ Net = $0\%$ Ratio of CP of A to B = $(0 - (-12)) : (20 - 0) = 12 : 20 = 3 : 5$ Total parts = 8 parts = ₹ 8000. CP of A = 3 parts = ₹ 3000. CP of B = 5 parts = ₹ 5000. Then proceed to find the target SP. ### Common Pitfall A common mistake is misinterpreting "overall profit of 25%" as applying only to article B, instead of the total cost price of both articles. ### Final Answer Therefore, the correct answer is **₹ 6400**.