Multiple choice

Divide Rs. 3,903 between A and B, such that A's share at the end of 7 years is equal to B's share at the end of 9 years at 4% p.a. rate of compound interest.

  1. Rs. 2,233; Rs. 1,670

  2. Rs. 2,125; Rs. 1,778

  3. Rs. 2,075; Rs. 1,828

  4. Rs. 2,028; Rs. 1,875
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A(1 + 0.04)^7 = B(1 + 0.04)^9. A = B(1.04)^2 = B(1.0816). A + B = 3903. 1.0816B + B = 3903. 2.0816B = 3903. B = 1875. A = 3903 - 1875 = 2028.

AI explanation

Let A's share be x and B's share be (3903 - x). Because A's amount after 7 years equals B's amount after 9 years at 4% compound interest, we equate their amounts using the compound interest formula: x(1 + 4/100)^7 = (3903 - x)(1 + 4/100)^9. Dividing both sides by (1 + 4/100)^7 gives x = (3903 - x)(1.04)^2, which simplifies to x = 1.0816(3903 - x). Solving for x yields 2.0816x = 4221.5808, so x is approximately Rs. 2028, making B's share Rs. 1875.

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