Ram borrowed Rs. $725$ from Shyam at the beginning of a year at interest. After $8$ months, he again borrowed RS. $362.50$ at a rate of interest double that the former sum bears. At the end of the year, the sum of interest on both loans is Rs. $43.50$. Find the first rate of interest per annum?

Using the Simple Interest formula, the interest on the first loan for a year equals (725 x R x 1) / 100, which is 7.25R. The interest on the second loan for 4 months, which is one-third of a year, at double the rate equals (362.50 x 2R x 1/3) / 100, resulting in 2.4167R. The sum of both interests is Rs. 43.50, so 7.25R + 2.4167R equals 43.50, which simplifies to 9.6667R = 43.50. Solving this equation gives a first interest rate of 4.5%.

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