Multiple choice

Shivam and Amit invest equal sum. Shivam invested on C.I. for two years at the rate of 15% p.a. and Amit invested 3/4th of sum at some rate of simple interest and remaining sum at the rate of 9% p.a. on simple interest. If interest received by both at the end of two years are equal, then find the interest earned by Amit?

  1. 8000

  2. 9000

  3. 10000

  4. can't be determined

  5. e) 12000 12000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Shivam's two-year compound interest is 32.25% of the invested sum. Amit's interest is equal to this amount, but the rate on the first three-fourths of his investment is unspecified. Since the common principal is also not given, the numerical interest cannot be determined.

AI explanation

Let the equal sum invested by both be P, so Shivam's compound interest is P times 0.15 squared plus P times 0.15, which equals 0.3225 times P. Amit's simple interest is 0.75 times P times R times 2 divided by 100 plus 0.25 times P times 9 times 2 divided by 100, which equals 0.015 times P times R plus 0.045 times P. Equating the interests gives 0.3225 times P equal to 0.015 times P times R plus 0.045 times P, meaning R is 18.5%. Since the principal sum P is never provided as a numerical value, the exact numerical interest earned by Amit cannot be calculated.

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