A gold bracelet is sold for ₹ 14500 at a loss of 20%. What is the cost price of the gold bracelet?

### Concept & Cost Price from Loss When an item is sold at a loss, the Selling Price (SP) is less than the Cost Price (CP). A 20% loss means the SP is only 80% of the original CP. $$ \text{CP} = \frac{\text{SP}}{\left(1 - \frac{\text{Loss \%}}{100}\right)} $$ ### Step-by-Step Solution * **Step 1:** Identify the known variables. * Selling Price (SP) = ₹ 14500 * Loss Percentage = 20% * **Step 2:** Formulate the equation. * A loss of 20% indicates that the item was sold for $(100\% - 20\%) = 80\%$ of its Cost Price. * $80\% \text{ of CP} = 14500$ * $0.80 \times \text{CP} = 14500$ * **Step 3:** Calculate the Cost Price. * $\text{CP} = \frac{14500}{0.80}$ * $\text{CP} = \frac{145000}{8}$ * $\text{CP} = ₹ 18125$ ### Exam Strategy & Shortcut Use fractional equivalents. $20\% \text{ loss} = \frac{1}{5} \text{ loss}$. This means for every 5 parts of CP, there is 1 part loss, resulting in an SP of 4 parts. If 4 parts = 14500, then 1 part = $\frac{14500}{4} = 3625$. The CP is 5 parts, so $5 \times 3625 = 18125$. ### Common Pitfall Many candidates mistakenly calculate 20% of the Selling Price (₹ 14500) and add it back to find the Cost Price. 20% of 14500 is 2900, leading to a wrong answer of 17400 (Option C is a trap for this exact mistake). ### Final Answer Therefore, the correct answer is **₹ 18125**.