The difference between compound and simple interest on a principal at 5% per annum for 2 years is Rs. 1.50. Find the sum_______?
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Answer: A. Rs.600
Explanation
The difference between compound and simple interest over two years is given by the formula principal times the square of the rate percentage. Substituting one point fifty for the difference and five percent for the rate gives one point fifty equals P times five over one hundred squared. Simplifying five over one hundred squared to one over four hundred and multiplying by one point fifty yields a principal sum of six hundred. The two-year interest variance formula provides a direct mathematical link between the principal and the interest rate percentage. Squaring five percent yields twenty-five over ten thousand, which simplifies to the fraction one over four hundred. Multiplying the interest difference by the denominator four hundred immediately isolates the unknown principal sum.
Option B produces an interest difference of one point twenty-five, which falls short of the required one point fifty. Option C yields an interest difference of one rupee when tested against the five percent two-year formula. Option D results in an interest difference of seventy-five paisa, failing to match the problem statement.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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