If the simple interest on a certain sum of money is 4/25 of the sum and the…

2023

If the simple interest on a certain sum of money is 4/25 of the sum and the rate percent equals the number years, then the rate of interest per annum is:

  1. A.

    10%

  2. B.

    6%

  3. C.

    5%

  4. D.

    4%

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Show answer & explanation

Correct answer: D

Key idea: simple interest = (P × R × T)/100 and the rate equals the number of years, so set R = T.

  1. Write the simple interest relation: (P × R × T)/100 = (4/25) × P.

  2. Since rate equals years, set T = R. Substitute to get (P × R^2)/100 = (4/25) × P.

  3. Cancel P from both sides: R^2/100 = 4/25.

  4. Multiply both sides by 100: R^2 = 100 × (4/25) = 16, so R^2 = 16.

  5. Take the positive square root (rate is positive): R = 4. Thus the rate per annum is 4%.

Check: (4 × 4)/100 = 16/100 = 4/25, which matches the given simple interest fraction.

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