Multiple choice

Two partner $A$ and $B$ together lend Rs. $84100$ at $5\%$ compounded annually. The amount which a gets at the end of $3$ years is the same as what $B$ gets at the end of $5$ years. Determine the ratio of Shares of $A$ and $B$

  1. $21 :20$
  2. $441: 400$
  3. $1 : 4$
  4. $5 : 21$
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B Correct answer
Explanation

Let A and B be the shares. A(1.05)^3 = B(1.05)^5. Thus A/B = (1.05)^2 = (21/20)^2 = 441/400.

AI explanation

Because compound interest yields the same final amount, the principal amounts inversely relate to the compound interest factors for the respective periods. Let the shares of A and B be in the ratio (1.05)^5 to (1.05)^3, which simplifies to (1.05)^2 to 1, or 1.1025 to 1. Multiplying by 400 to convert to whole numbers gives a ratio of 441 to 400.

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