Question 1

A and B started a business by investing ₹ 2400 and ₹ 3600 respectively. At the end of 4th month from the start of the business, C joined with ₹ 'X'. After 8 months from the start of the business. B withdrew ₹600. If C's share is ₹ 8000 in the annual…

Accepted Answer

Concept & Reverse Profit Sharing: When the final profit share and total profit are known but an investment is unknown, set up an equation equating the ratio of the unknown equivalent capital to the known equivalent capital with the ratio of their respective profits. \frac{C's Capital}{(A+B)'s Capital} = \frac{C's Profit}{(A+B)'s Profit} Step-by-Step Solution: • Given: • Business duration is 12 months (annual profit). • A's investment = ₹2400 for 12 months. • B's investment = ₹3600 for 8 months, then withdraws ₹600, meaning (3600 - 600) = ₹3000 for the remaining 4 months. • C's investment = ₹X for 8 months (joined after 4 months). • Total profit = ₹22,500; C's share = ₹8,000. • Calculation: • A's equivalent capital = 2400 × 12 = 28800 • B's equivalent capital = (3600 × 8) + (3000 × 4) = 28800 + 12000 = 40800 • C's equivalent capital = 8X • Sum of A and B's equivalent capitals = 28800 + 40800 = 69600 • Sum of A and B's profit = 22500 - 8000 = 14500 • Equating the ratios: (8X/69600) = (8000/14500) • Simplify the profit ratio: (8000/14500) = (80/145) = (16/29) • (8X/69600) = (16/29) • 8X = 69600 × ((16/29)) • 69600 / 29 = 2400 • 8X = 2400 × 16 = 38400 • X = (38400/8) = 4800 Exam Strategy & Shortcut: Instead of finding C's proportion over the *total* sum (which requires adding 8X to the denominator), compare C directly against the sum of A and B. This keeps the unknown variable X isolated in the numerator, solving the equation faster. Common Pitfall: A frequent error is calculating C's investment time as 4 months instead of 8 months. "At the end of 4th month... C joined" means C was active for the remaining 12 - 4 = 8 months. Final Answer: Therefore, the correct answer is ₹ 4800.

Question 2

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 answer…

Accepted Answer

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 Investment × 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 × 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 × 18. • Combining all three statements gives us the total equivalent capital (85000 × 24 + 250000 × 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 × Time and Total Inv × 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.

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