Multiple choice

Naveen divides Rs 30563 among Sona, Mona, and Kavita, so that if the amounts being invested at 4% simple interest, the amounts received after 2, 3 and 4 years by Sona, Mona, and Kavita respectively is equal. Find the share of Mona?

  1. Rs. 10179

  2. Rs. 11379

  3. Rs. 11579

  4. Rs. 11879

  5. Rs. 12179
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A Correct answer
Explanation

Let shares be x, y, z for 2, 3, 4 years at 4% SI. Equal amounts means x(1 + 0.08) = y(1 + 0.12) = z(1 + 0.16). So 1.08x = 1.12y = 1.16z. Ratio x:y:z = 1/1.08 : 1/1.12 : 1/1.16 = 100/108 : 100/112 : 100/116 = 25/27 : 25/28 : 25/29. Total = 25/27 + 25/28 + 25/29 = 25(1/27 + 1/28 + 1/29). Mona's share = (25/28) / [25(1/27 + 1/28 + 1/29)] × 30563. After calculation: share is proportional to 1/(1 + 0.04t). Ratio x:y:z = 1/1.08 : 1/1.12 : 1/1.16. Multiplying by LCM: 26.57 : 25.59 : 24.78. Total parts ≈ 76.94. Mona's share = 25.59/76.94 × 30563 ≈ 10179.

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