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 percent is the earned profit? I. 10% discount is offered on the marked price. II. If no discount is given, the profit will be 30%.

### Concept & Strategy Profit percentage is derived from the ratio of Cost Price (CP) to Selling Price (SP). In percentage-only problems, assuming a base value like 100 for CP simplifies finding the relationships. $$ \text{Profit \%} = \left( \frac{\text{SP} - \text{CP}}{\text{CP}} \right) \times 100 $$ ### Step-by-Step Solution * **Target:** Find actual Profit %. Let $\text{CP} = 100$. * **Evaluate Statement I:** 10% discount is offered on Marked Price (MP). * $\text{SP} = \text{MP} - 0.10\text{MP} = 0.90\text{MP}$. We do not know the relationship between MP and CP. Not sufficient. * **Evaluate Statement II:** If no discount is given, profit is 30%. * No discount means $\text{SP} = \text{MP}$. * Profit = 30% of CP. So, $\text{MP} = 100 + 30 = 130$. * This gives us the MP relative to CP, but not the actual SP since the actual scenario might involve a discount. Not sufficient. * **Evaluate Both Together:** * From Statement II, we established that $\text{MP} = 130$ (when $\text{CP} = 100$). * From Statement I, we know the actual SP involves a 10% discount on this MP. * Actual $\text{SP} = 130 - (10\% \text{ of } 130) = 130 - 13 = 117$. * Actual Profit = $\text{SP} - \text{CP} = 117 - 100 = 17$. * Actual Profit % = 17%. Both statements are required. ### Exam Strategy & Shortcut Whenever a problem asks for a final percentage and gives only intermediate percentage relationships (like markups and discounts), you need the complete chain from CP to MP to SP. Statement II gives the CP to MP link, and Statement I gives the MP to SP link. ### Common Pitfall Assuming Statement II alone is the answer. It only describes a hypothetical "no discount" scenario, not the actual earned profit which includes the standard discount practice mentioned in I. ### Final Answer Therefore, the correct answer is **if the data in both Statements I and II together are necessary to answer the question.**.