Gain Percent 808Bec

1. **Problem 9:** A fruit seller buys lemons at P2 for a rupee and sells them at P5 for three rupees. Find his gain percent. 2. **Step 1:** Understand the cost price (CP) and selling price (SP). - Cost price of 2 lemons = 1 rupee, so cost price of 1 lemon = $\frac{1}{2}$ rupee. - Selling price of 5 lemons = 3 rupees, so selling price of 1 lemon = $\frac{3}{5}$ rupee. 3. **Step 2:** Calculate gain per lemon. $$\text{Gain} = \text{SP} - \text{CP} = \frac{3}{5} - \frac{1}{2}$$ 4. **Step 3:** Find a common denominator and subtract. $$\frac{3}{5} = \frac{6}{10}, \quad \frac{1}{2} = \frac{5}{10}$$ $$\text{Gain} = \frac{6}{10} - \frac{5}{10} = \frac{1}{10}$$ 5. **Step 4:** Calculate gain percent. $$\text{Gain \%} = \left(\frac{\text{Gain}}{\text{CP}}\right) \times 100 = \left(\frac{\frac{1}{10}}{\frac{1}{2}}\right) \times 100$$ 6. **Step 5:** Simplify the fraction. $$\left(\frac{\frac{1}{10}}{\frac{1}{2}}\right) = \frac{1}{10} \times \frac{2}{1} = \frac{2}{10} = \frac{1}{5}$$ 7. **Step 6:** Calculate the percentage. $$\frac{1}{5} \times 100 = 20\%$$ 8. **Answer for problem 9:** Gain percent is 20% (Option C). --- 9. **Problem 10:** Selling price of 40 articles equals cost price of 50 articles. Find loss or gain percent. 10. **Step 1:** Let cost price of 1 article = $C$. - Then cost price of 50 articles = $50C$. - Selling price of 40 articles = $50C$ (given). 11. **Step 2:** Find selling price of 1 article. $$\text{SP per article} = \frac{50C}{40} = \frac{5C}{4} = 1.25C$$ 12. **Step 3:** Compare SP and CP per article. - CP = $C$ - SP = $1.25C$ 13. **Step 4:** Since SP > CP, there is a gain. 14. **Step 5:** Calculate gain percent. $$\text{Gain} = \text{SP} - \text{CP} = 1.25C - C = 0.25C$$ $$\text{Gain \%} = \left(\frac{0.25C}{C}\right) \times 100 = 25\%$$ 15. **Answer for problem 10:** 25% gain (Option D).