Multiple choice

A sum of Rs. 2,50,000 is divided among three individuals - X, Y, and Z - in such a way that they receive amounts in the ratio of 3 : 4 : 5, respectively. X further invests his share in a scheme that offers a simple interest rate of 8% per annum for 2 years. Y invests his share in a scheme that offers a compound interest rate of 10% per annum for 3 years. Z keeps his share as cash. Determine the total interest earned by X and Y, after the specified time period.

  1. Rs. 49,180.54

  2. Rs. 37,583.33

  3. Rs. 29,180.54

  4. Rs. 20,180.54
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total sum is 2,50,000. Ratio 3:4:5 means total parts = 12. X's share = (3/12)*2,50,000 = 62,500. Y's share = (4/12)*2,50,000 = 83,333.33. Interest for X (SI) = 62,500 * 0.08 * 2 = 10,000. Interest for Y (CI) = 83,333.33 * ((1.1)^3 - 1) = 83,333.33 * 0.331 = 27,583.33. Total interest = 10,000 + 27,583.33 = 37,583.33.

AI explanation

Let the shares of X, Y and Z be 3x, 4x and 5x, so 12x = 250000 and x = 20833.33. X's share is 62500, and using the simple interest formula of P * R * T / 100, the interest is (62500 * 8 * 2) / 100 = 10000. Y's share is 83333.33, and using the compound interest formula of P * [(1 + R/100)^T - 1], the interest is 83333.33 * [(1.1)^3 - 1] = 27583.33. The total interest is 10000 + 27583.33 = 37583.33. Therefore, the answer is Rs. 37,583.33.

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