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. What is the percent profit earned by selling the product? I. The profit earned was ₹ 50. II. Had it been sold for ₹ 310, the profit would have been ₹ 70.

### Concept & Formula To find the percent profit, we need both the absolute Profit and the Cost Price (CP). $$ \text{Percent Profit} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 $$ ### Step-by-Step Solution * **Evaluate Statement I:** Profit = ₹ 50. We don't have the CP. Not sufficient. * **Evaluate Statement II:** If New SP = ₹ 310, then New Profit = ₹ 70. * We know $\text{CP} = \text{New SP} - \text{New Profit} = 310 - 70 = \text{₹ } 240$. * However, we don't know the *original* profit earned to find the original percent profit. Not sufficient. * **Evaluate Both Together:** * From Statement II, we found $\text{CP} = \text{₹ } 240$. * From Statement I, we know the original Profit = ₹ 50. * Now we have both components: $\text{Percent Profit} = (50 / 240) \times 100$. This gives a specific value. * Both statements together are necessary and sufficient. ### Exam Strategy & Shortcut Identify the variables needed: Profit and CP. Statement I gives Profit. Statement II gives a scenario to calculate CP (SP - Profit = CP). Together, they provide both needed pieces. ### Common Pitfall Thinking Statement II alone is sufficient by assuming the ₹ 70 profit is the profit meant in the question, rather than a hypothetical scenario. ### Final Answer Therefore, the correct answer is **if the data in both Statements I and II together are necessary to answer the question.**.