Directions: Each of these questions is followed by three statements. You have to study the question and all the three statements given to decide whether any information provided in the statement(s) is redundant and can be dispensed with while answering the given question. Three friends P, Q and R started a partnership business investing money in the ratio of $5 : 4 : 2$ respectively for a period of 3 years. What is the amount received by P as his share in the total profit? I. Total amount invested in the business is ₹ 22000. II. Profit earned at the end of 3 years is $\frac{3}{8}$ of the total investment. III. The average amount of profit earned per year is ₹ 2750.

### Concept & Logic To find an individual partner's share in a partnership, we need two key pieces of information: the ratio of their investments (which is given as $5 : 4 : 2$) and the total profit earned by the business. The question asks us to identify which statements provide redundant information to find this total profit. ### Step-by-Step Solution * **From Statement III:** We are given the average profit per year is ₹ 2750. * Total profit for 3 years = $3 \times 2750 = \text{₹ } 8250$. * With the total profit and the investment ratio, we can calculate P's share. Therefore, if we use Statement III, Statements I and II are redundant (dispensable). * **From Statements I and II together:** * Statement I gives the total investment = ₹ 22000. * Statement II states the total profit is $\frac{3}{8}$ of the total investment. * Total profit = $\frac{3}{8} \times 22000 = \text{₹ } 8250$. * Again, we have the total profit and can find P's share. Therefore, if we use Statements I and II, Statement III is redundant. * **Conclusion:** The redundancy is an "either/or" situation. We can dispense with either Statement III alone, or Statements I and II together. ### Exam Strategy & Shortcut In Data Sufficiency questions involving "redundancy", identify all independent pathways to reach the solution. Here, Path A is (Statement III) and Path B is (Statements I + II). Since either path works, the other is redundant. ### Common Pitfall A common mistake is selecting only one of the redundant sets (e.g., thinking only III is redundant because I and II are presented first) without considering that the reverse is also true. ### Final Answer Therefore, the correct answer is **Either III only, or I and II together**.