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. What is Neeta's share in the profit of ₹ 50000 earned at the end of 2 years in a joint business run by Neeta, Seeta and Geeta? I. Neeta invested ₹ 85000 to start the business. II. Seeta and Geeta joined Neeta's business after six months, investing amounts in the ratio of $3 : 5$. III. Total amount invested by Seeta and Geeta is ₹ 2.5 lakh.

### Concept & Ratio of Equivalent Capitals To calculate a partner's share in the total profit, we need the ratio of their "equivalent capital" (which is $\text{Investment} \times \text{Time}$). For Neeta's share, we specifically need Neeta's equivalent capital relative to the total equivalent capital of all partners combined. ### Step-by-Step Solution * **From the main question:** Total profit = ₹ 50,000. Total time = 2 years (24 months). * **From Statement I:** Neeta's investment is ₹ 85,000. She invested for the full 24 months. * Neeta's equivalent capital = $85000 \times 24$. * **From Statement III:** Seeta and Geeta's combined investment is ₹ 2,50,000 (2.5 lakh). * **From Statement II:** Seeta and Geeta joined after 6 months, meaning their investment time is $24 - 6 = 18$ months. * Seeta and Geeta's combined equivalent capital = $250000 \times 18$. * Combining all three statements gives us the total equivalent capital ($85000 \times 24 + 250000 \times 18$) and Neeta's individual part, allowing us to find her exact share. * **Checking for Redundancy:** * Discarding I: We lose Neeta's investment amount. * Discarding II: We lose the time duration (18 months) for Seeta and Geeta. * Discarding III: We lose the combined investment amount of Seeta and Geeta. * Therefore, no single statement can be completely dispensed with. ### Exam Strategy & Shortcut In Data Sufficiency, do not waste time fully calculating the final numerical answer. Once you confirm you have the necessary variables (Neeta's Inv $\times$ Time and Total Inv $\times$ Time), stop and evaluate if any single statement can be dropped. If dropping a statement removes a crucial variable (like time), it is fully required. ### Common Pitfall A common mistake is realizing that the $3 : 5$ ratio in Statement II is not needed to find *Neeta's* share, and thus incorrectly assuming Statement II is completely redundant. You must read the *entire* statement to ensure no other critical data (like the 6-month delay) is lost by dispensing with it. ### Final Answer Therefore, the correct answer is **Information in all the three statements is required to answer the question**.