The difference between the simple interest received from two different sources…

2024

The difference between the simple interest received from two different sources on Rs. 3 lakhs for 2 years is Rs. 1,500. The difference between their rates of interest is

  1. A.

    0.20%

  2. B.

    0.3%

  3. C.

    0.25%

  4. D.

    0.4%

Show answer & explanation

Correct answer: C

Concept:

For two simple-interest rates applied to the same principal P over the same time T, the two interest amounts differ only through the difference between the rates: SI1 − SI2 = P × T × (R1 − R2) / 100, where SI1 and SI2 are the two interest amounts and R1, R2 are their annual rates.

Application:

  1. Let R1 and R2 be the two annual rates of interest, with P = Rs. 3,00,000 and T = 2 years.

  2. Substitute the given interest difference into the formula: 3,00,000 × 2 × (R1 − R2) / 100 = 1,500.

  3. Simplify the left side: 6,000 × (R1 − R2) = 1,500.

  4. Divide both sides by 6,000: (R1 − R2) = 1,500 / 6,000 = 0.25%.

Cross-check:

Substituting (R1 − R2) = 0.25% back into the formula gives 3,00,000 × 2 × 0.25 / 100 = Rs. 1,500, which matches the given difference — confirming the rate difference is consistent with the stated data.

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