Gain Loss Percentage Fd1152

1. **Problem Statement:** X sells two articles for $4000$ each with no overall loss or gain. One article is sold at a gain of $25\%$. We need to find the loss percentage on the other article. 2. **Understanding the problem:** If the total transaction has no loss or gain, the total cost price equals the total selling price. 3. **Let the cost prices of the two articles be $C_1$ and $C_2$.** Selling price of each article is $4000$. 4. **Given:** - First article sold at $25\%$ gain. - So, selling price $S_1 = 4000 = C_1 + 0.25 C_1 = 1.25 C_1$. 5. **Calculate $C_1$:** $$ C_1 = \frac{4000}{1.25} = 3200 $$ 6. **Total selling price:** $$ S_1 + S_2 = 4000 + 4000 = 8000 $$ 7. **Since no overall gain or loss:** $$ C_1 + C_2 = 8000 $$ $$ 3200 + C_2 = 8000 $$ $$ C_2 = 8000 - 3200 = 4800 $$ 8. **Selling price of second article:** $$ S_2 = 4000 $$ 9. **Loss on second article:** $$ \text{Loss} = C_2 - S_2 = 4800 - 4000 = 800 $$ 10. **Loss percentage:** $$ \text{Loss \%} = \frac{\text{Loss}}{C_2} \times 100 = \frac{800}{4800} \times 100 $$ 11. **Simplify loss percentage:** $$ = \frac{\cancel{800}}{6 \times \cancel{800}} \times 100 = \frac{1}{6} \times 100 = 16.67\% $$ **Final answer:** The other article is sold at a loss of $16.67\%$.