A certain sum amounts to ₹57,600 at the end of five years and to ₹48,960 at the end of three years both being at simple interest. Find the rate of interest.

Sure, here is the step by step solution:

Step 1: We know that the formula for simple interest is I = PRT/100, where P is the principal amount, R is the rate of interest, and T is the time in years.

Step 2: Given that the sum amounts to ₹57,600 at the end of five years and ₹48,960 at the end of three years, we can infer that the interest for two years is ₹57,600 - ₹48,960 = ₹8,640.

Step 3: Now, we can use the formula for simple interest to find the rate of interest. We know that the interest for two years is ₹8,640, and the principal amount is ₹48,960 (since this is the amount at the end of three years without the interest for the last two years).

Step 4: Substituting these values into the formula, we get 8640 = 48960 * R * 2 / 100.

Step 5: Solving this equation for R, we get R = (8640 * 100) / (48960 * 2) = 8.8%.

So, the rate of interest is 8.8%.