Multiple choice

A, B and C borrow Rs. 29,200 in all at 4% simple interest and pay back equal amounts in full settlement of their respective debts after 5, 10 and 15 years, respectively. Find the sum borrowed by C.

  1. Rs. 11,200

  2. Rs. 9,600

  3. Rs. 8,400

  4. Rs. 7,600
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C Correct answer
Explanation

Let A, B, C borrow x, y, z. x + y + z = 29200. Amounts are equal: x(1 + 0.04*5) = y(1 + 0.04*10) = z(1 + 0.04*15). 1.2x = 1.4y = 1.6z. x = 1.6z/1.2 = 4/3 z. y = 1.6z/1.4 = 8/7 z. (4/3 + 8/7 + 1)z = 29200. (28/21 + 24/21 + 21/21)z = 29200. 73/21 z = 29200. z = 29200 * 21 / 73 = 400 * 21 = 8400.

AI explanation

Since each person pays back the same equal amount, their principal amounts are inversely proportional to their total time periods. Given the time periods of 5, 10, and 15 years, the inverse ratio is calculated as one fifth is to one tenth is to one fifteenth, which simplifies to 6 to 3 to 2. The total ratio parts equal 11, and multiplying the total debt of Rs. 29200 by 2 divided by 11 gives the sum borrowed by C as Rs. 8400.

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