Simple interest on a certain sum of money for 3 years at 8% per annum is half…

2023

Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:

  1. A.

    Rs. 1550

  2. B.

    Rs. 1650

  3. C.

    Rs. 1750

  4. D.

    Rs. 1759

Attempted by 1 students.

Show answer & explanation

Correct answer: C

Step-by-Step Solution

To find the sum placed on simple interest, we need to break the problem into two parts: calculating the compound interest first, then using that to find the simple interest and the required sum.

  1. Calculate the Compound Interest (CI) on Rs. 4000 for 2 years at 10%:

    • Formula: Amount = P * (1 + R/100)^T

    • Amount = 4000 * (1 + 10/100)^2

    • Amount = 4000 * (1.1)^2 = 4000 * 1.21 = Rs. 4840

    • CI = Amount - Principal = 4840 - 4000 = Rs. 840

  2. Calculate the Simple Interest (SI) for the unknown sum:

    • The problem states that the SI is half of the CI.

    • SI = CI / 2 = 840 / 2 = Rs. 420

  3. Calculate the sum (Principal) for the simple interest:

    • Formula: SI = (P * R * T) / 100

    • 420 = (P * 8 * 3) / 100

    • 420 = 24P / 100

    • P = (420 * 100) / 24

    • P = 42000 / 24 = Rs. 1750

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