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. Ravi, Gagan and Nitin are running a business firm in partnership. What is Gagan's share in the profit earned by them? I. Ravi, Gagan and Nitin invested the amounts in the ratio of $2 : 4 : 7$. II. Nitin's share in the profit is ₹ 8750.

### Concept & Logic To find the profit share of an individual in a partnership, we need the ratio of their investments (or equivalent investments over time) and either the total profit or the exact profit share of at least one other partner. ### Step-by-Step Solution * **From Statement I:** We know the investment ratio of Ravi, Gagan, and Nitin is $2 : 4 : 7$. Assuming the time periods are the same, this is also the profit ratio. However, without any absolute profit amount, we cannot find Gagan's share. Statement I alone is insufficient. * **From Statement II:** We know Nitin's profit share is ₹ 8750. Without knowing the profit ratio or total profit, we cannot find Gagan's share. Statement II alone is insufficient. * **Combining I and II:** From I, the profit ratio is $2 : 4 : 7$. From II, Nitin's share (7 parts) is ₹ 8750. * We can calculate the value of 1 part: $\frac{8750}{7} = 1250$. * Gagan's share is 4 parts: $4 \times 1250 = 5000$. * Since we can find the answer by combining both statements, both I and II are necessary. ### Exam Strategy & Shortcut In data sufficiency, you don't need to calculate the final answer. As soon as you realize that you have the ratio and one absolute value, you know the data is sufficient. Combine the statements immediately mentally to save time. ### Common Pitfall Assuming the total profit is given or missing the fact that a ratio alone cannot give an absolute value. ### Final Answer Therefore, the correct answer is **if the data in both Statements I and II together are necessary to answer the question.**