Directions: Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the question. Read both the statements and Give answer (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question; Give answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question; Give answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question; Give answer (d) if the data even in both Statements I and II together are not sufficient to answer the question; Give answer (e) if the data in both Statements I and II together are necessary to answer the question. By selling a product for ₹ 200, how much profit was earned? I. The profit was 25 percent of the cost price. II. 12.5 percent profit would have been earned if the product had been sold for ₹ 180.

### Concept & Logic The actual Profit amount is the difference between Selling Price (SP) and Cost Price (CP). Since the actual SP is given (₹ 200), we only need to find a unique CP to answer the question. ### Step-by-Step Solution * **Target:** Find actual Profit (in ₹). Given actual $\text{SP} = \text{₹ } 200$. * **Evaluate Statement I:** Profit = 25% of CP. * $\text{SP} = \text{CP} + 0.25\text{CP} = 1.25\text{CP}$. * $200 = 1.25\text{CP} \Rightarrow \text{CP} = \frac{200}{1.25} = 160$. * Actual Profit = $200 - 160 = \text{₹ } 40$. Statement I alone is sufficient. * **Evaluate Statement II:** Hypothetical $\text{SP} = \text{₹ } 180$ yields a 12.5% profit. * $180 = \text{CP} + 0.125\text{CP} = 1.125\text{CP}$. * $\text{CP} = \frac{180}{1.125} = 160$. * Now that we know $\text{CP} = 160$, we use the original SP to find the actual profit: $200 - 160 = \text{₹ } 40$. Statement II alone is also sufficient. ### Exam Strategy & Shortcut Recognize that finding CP is the sole missing link. Any statement that provides an SP and its corresponding profit percentage (whether real or hypothetical) allows you to calculate the CP directly. Thus, either statement works independently. ### Common Pitfall Solving both statements completely. In Data Sufficiency, once you realize a statement gives you the single variable you need (CP), you can stop calculating and declare it sufficient. ### Final Answer Therefore, the correct answer is **if the data either in Statement I or in Statement II alone are sufficient to answer the question;**.