A starts with ₹ 4,000 for 12 months; B joins after 3 months with ₹ 8,000 for 9 months; C invests ₹ 20,000 but only for the last 2 months. At year end, profit is ₹ 16,800. How should the profit be divided among A, B, and C?
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AA = ₹ 5,040, B = ₹ 7,560, C = ₹ 4,200
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BA = ₹ 7,560, B = ₹ 5,040, C = ₹ 4,200
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CA = ₹ 4,200, B = ₹ 7,560, C = ₹ 5,040
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DA = ₹ 4,200, B = ₹ 5,040, C = ₹ 7,560
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EA = ₹ 5,600, B = ₹ 7,000, C = ₹ 4,200
Answer
Correct Answer: A = ₹ 5,040, B = ₹ 7,560, C = ₹ 4,200
Explanation
Introduction / Context: Different start times and durations require capital-time weights for each partner. Profit division then follows those weights.
Given Data / Assumptions:
- A: 4,000 for 12 months.
- B: 8,000 for 9 months.
- C: 20,000 for 2 months.
- Total profit = ₹ 16,800.
Concept / Approach: Compute weights: A = 4,000*12, B = 8,000*9, C = 20,000*2. Reduce to a simple ratio and split the profit accordingly.
Step-by-Step Solution: A's weight = 48,000; B's weight = 72,000; C's weight = 40,000. Ratio = 48,000 : 72,000 : 40,000 = 6 : 9 : 5. Total parts = 6 + 9 + 5 = 20; each part = 16,800 / 20 = ₹ 840. Shares: A = 6*840 = ₹ 5,040; B = 9*840 = ₹ 7,560; C = 5*840 = ₹ 4,200.
Verification / Alternative check: Sum = 5,040 + 7,560 + 4,200 = ₹ 16,800, confirming the division.
Why Other Options Are Wrong: Options that swap roles or change one figure break the 6 : 9 : 5 ratio implied by the investment schedule.
Common Pitfalls: Forgetting C invests only for 2 months, or mistakenly assuming all invested for the full year.
Final Answer: A = ₹ 5,040, B = ₹ 7,560, C = ₹ 4,200