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 Nikita's share in the profit of ₹ 50000 earned in the business run by her in partnership with Shalini? I. Nikita invested an amount 150% of the amount invested by Shalini. II. Amount invested by Shalini is two-thirds of the amount invested by Nikita.

### Concept & Logic Profit is distributed in the ratio of investments (assuming time periods are equal). If we can establish the ratio of Nikita's investment to Shalini's investment, we can divide the total profit of ₹ $50,000$ to find Nikita's exact share. ### Step-by-Step Solution * Given: Total profit = ₹ $50,000$. * **From Statement I:** Nikita invested $150\%$ of Shalini's amount. * Let Shalini's investment be $x$. * Nikita's investment = $1.5x$. * Ratio (Nikita : Shalini) = $1.5x : x = 3 : 2$. * We have the ratio and the total profit, so we can find Nikita's share. Statement I alone is sufficient. * **From Statement II:** Shalini's investment is $\frac{2}{3}$ of Nikita's. * Let Nikita's investment be $y$. * Shalini's investment = $\frac{2}{3}y$. * Ratio (Nikita : Shalini) = $y : \frac{2}{3}y = 3 : 2$. * We have the ratio and the total profit, so we can find Nikita's share. Statement II alone is sufficient. ### Exam Strategy & Shortcut Notice that Statement I ($150\% = \frac{3}{2}$) and Statement II (Shalini is $\frac{2}{3}$ of Nikita, meaning Nikita is $\frac{3}{2}$ of Shalini) are mathematically identical statements. Since both give the exact same investment ratio, and the total profit is already known, either statement alone will suffice. ### Common Pitfall Wasting time calculating the final answer (Nikita's share = $\frac{3}{5} \times 50000 = 30000$). In Data Sufficiency, once you know you *can* find the answer, stop calculating and mark the option. ### 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;**.