Multiple choice

How can Rs. 3903 be divided between A and B today so 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. 2233, Rs. 1670

  2. Rs. 2125, Rs. 1778

  3. Rs. 2075, Rs. 1828

  4. Rs. 2028, Rs. 1875

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A * (1 + 0.04)^7 = B * (1 + 0.04)^9. This simplifies to A = B * (1.04)^2 = B * 1.0816. A + B = 3903. Substituting A: B * 1.0816 + B = 3903 => 2.0816 * B = 3903 => B = 1875. A = 3903 - 1875 = 2028.

AI explanation

Let A's share be x and B's share be 3903 minus x. Using the compound interest formula, x times 1.04 to the power of 7 equals (3903 minus x) times 1.04 to the power of 9. Simplifying this gives x divided by (3903 minus x) equals 1.04 squared, which is 676 divided by 625. Solving for x yields 1301x equals 2639028, so x is 2028 and B's share is 1875.

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