Multiple choice

The simple and compound interest obtained at the rate of x% and y% on a sum of Rs. 15,000 is Rs. 2700 and Rs. 4965, respectively. If the time period for simple interest was 2 years and for compound interest was 3 years, then which of the following is correct, given that the interest was calculated yearly? (i) xy = 90 (ii) x + y = 19 (iii) x – y = 1 (iv) y – x = -1 (v) x2 + y = 91

  1. Only (i) and (ii)

  2. Only (i), (ii) and (v)

  3. Only (ii), (iii) and (v)

  4. Only (iii) and (iv)

  5. All of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For simple interest, 15000 * x * 2 / 100 = 2700, so x = 9. For compound interest, 15000 * (1 + y/100)^3 - 15000 = 4965. Solving (1 + y/100)^3 = 1.331 gives 1 + y/100 = 1.1, so y = 10. Checking the options: (i) xy = 90 (True), (ii) x + y = 19 (True), (v) x^2 + y = 81 + 10 = 91 (True).

AI explanation

The simple interest rate x is found by dividing 2700 by 15000 to get 0.18, or 9% over 2 years, making x = 9. For the compound interest, 15000 times (1 plus y/100) cubed equals 19965, so (1 plus y/100) cubed equals 1.331, which makes the rate y = 10. Substituting these values, xy equals 90, x plus y equals 19, and x squared plus y equals 91; therefore, statements (i), (ii), and (v) are correct.

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