Multiple choice

Passage

Schemes Time (In Years) Rate of Interest P 20 x 2 - 8x - 20 = 0 Q y - 6 = 0 16% R 30 ---- Note: 1. If Time > Rate of Interest, then Simple Interest should be considered in any scheme. 2. If Time ≤ Rate of Interest, then Compound Interest should be considered in any scheme. 3. Some values are missing; you have to calculate them based on the question. 4. A and B are two colleagues who invested their amounts in scheme P and scheme Q, respectively. B invested Rs. 18,000, and the interest earned and sum invested in P is same. 5. A also invested some money in scheme R on Simple Interest, and the interest earned by her is same as the profit earned by scheme P. 6. Take positive values of equations for time and rate of interest. 7. The rate of interest in scheme R is less than the rate of interest in scheme P and is not a multiple of 3.

The ratio of investment of A and B in schemes P and Q is 5 : 6, respectively. If A invested the sum for the whole duration in scheme P, then the rate at which A invested in scheme P is what percent of the actual simple interest rate of scheme P?

  1. 15%

  2. 20%

  3. 50%

  4. 80%

  5. 100%
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C Correct answer
AI explanation

Solving 2x - 8x - 20 = 0 is not possible to yield a valid time and rate based on the question text, indicating the equation is missing its squared term. Working backwards from the assumption that the intended equation is 2x^2 - 8x - 20 = 0, we factor it as 2(x - 5)(x + 2) = 0 to get x = 5. Solving y - 6 = 0 gives y = 6, meaning B's investment of Rs. 18,000 is at 16% simple interest for 6 years, earning Rs. 17,280. Since the question states the ratio of investment is 5:6, A's investment is (5/6) * 18000 = Rs. 15,000. We are told the interest earned equals the sum invested, so A invests 15000 and earns 15000, which makes the asked ratio 15000 / 30000 = 0.5, or 50%. The result is 50%.

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