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. A man mixes two types of rice (X and Y) and sells the mixture at the rate of ₹ 17 per kg. Find his profit percentage. I. The rate of X is ₹ 20 per kg. II. The rate of Y is ₹ 13 per kg.

### Concept & Formula Profit percentage depends on both the Selling Price (SP) and the Cost Price (CP) of the mixture. $$ \text{Profit \%} = \left( \frac{\text{SP} - \text{CP}}{\text{CP}} \right) \times 100 $$ ### Step-by-Step Solution * **Given:** SP of the mixture = ₹ 17 per kg. We need the CP of the mixture to find the profit percentage. * **Evaluate Statement I:** Rate of X = ₹ 20 per kg. No information about Y or the mixing ratio. Not sufficient. * **Evaluate Statement II:** Rate of Y = ₹ 13 per kg. No information about X or the mixing ratio. Not sufficient. * **Evaluate Both Together:** We have the individual rates (₹ 20/kg and ₹ 13/kg), but we do NOT have the ratio in which types X and Y are mixed. * The CP of the mixture depends entirely on the ratio of X to Y. * Since the ratio is unknown, the CP cannot be determined, and thus the profit percentage cannot be found. ### Exam Strategy & Shortcut Recognize that mixture problems require three components to find an average price or profit: the price of both ingredients and their mixing ratio (or quantities). If the ratio is missing, the problem is unsolvable. ### Common Pitfall Assuming they are mixed in equal quantities (1:1 ratio) just because a ratio isn't given. Never assume information not explicitly stated. ### Final Answer Therefore, the correct answer is **if the data even in both Statements I and II together are not sufficient to answer the question;**.