Multiple choice

If Rs. 11,498 divided into two parts, A and B, such that the first part after 11 years is equal to the second part B after 13 years, compound interest being 14% per annum compounded yearly, then what is the value of A and B, respectively?

  1. Rs. 6,598; Rs. 5,000

  2. Rs. 6,235; Rs. 5,300

  3. Rs. 6,498; Rs. 5,000

  4. Rs. 5,498; Rs. 6,000

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

A * (1.14)^11 = B * (1.14)^13. This implies A = B * (1.14)^2 = B * 1.2996. A + B = 11498. Substituting A: 1.2996B + B = 11498, so 2.2996B = 11498, B = 5000. Then A = 11498 - 5000 = 6498.

AI explanation

Using the compound interest formula A(1 + 0.14)^11 = B(1 + 0.14)^13. This simplifies to A = B(1.14)^2, which means A = 1.2996B. Substituting this into the total sum equation A + B = 11498 gives 1.2996B + B = 11498. Solving for B gives 2.2996B = 11498, so B = 5000. Substituting B back into the total gives A = 6498. The value of A and B, respectively, is Rs. 6,498 and Rs. 5,000.

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