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Quantity A: Find the sum invested at 8%. A part of ₹16,000 is invested at 8% and the remaining part at 12% for 3 years under simple interest. The total interest after 3 years is ₹4,680. Quantity B: The amount if ₹8,000 is invested at double the rate for 1 year. The amount invested under simple interest doubles itself in 16 years. Compare Quantity A and Quantity B.

1. Quantity A ≥ Quantity B
2. Quantity A ≤ Quantity B
3. Quantity A = Quantity B or no relationship can be established
4. Quantity A > Quantity B

Correct answer: Quantity A = Quantity B or no relationship can be established

Solution

Let the amount invested at 8% be x, so the remaining is 16000 - x. Using simple interest for 3 years gives a unique x, but Quantity A asks for the sum invested at 8%, not a directly comparable final amount. Quantity B is a different amount based on a separate rate condition, so the relationship cannot be uniquely established from the given information.

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