The difference between compound interest and simple interest on a sum of money for 2 yearsat 10% p.a. is ` 300. Find the sum.

Sure, let's solve this step by step.

Step 1: Understand the problem The problem is asking us to find the principal amount (the sum of money) given that the difference between compound interest and simple interest for 2 years at 10% per annum is 300.

Step 2: Use the formula for compound interest and simple interest The formula for simple interest is SI = PRT/100, where P is the principal amount, R is the rate of interest, and T is the time in years. The formula for compound interest is CI = P(1 + R/100)^T - P, where P is the principal amount, R is the rate of interest, and T is the time in years.

Step 3: Set up the equation According to the problem, CI - SI = 300. We can substitute the formulas from step 2 into this equation to get: P(1 + R/100)^T - P - PRT/100 = 300

Step 4: Plug in the given values We know that R = 10, T = 2, and CI - SI = 300. So, we can plug these values into the equation to get: P(1 + 10/100)^2 - P - P102/100 = 300 Solving this equation gives us P(1.1)^2 - P - P*0.2 = 300 This simplifies to 1.21P - P - 0.2P = 300 This further simplifies to 0.21P = 300

Step 5: Solve for P Finally, we can solve for P by dividing both sides of the equation by 0.21 to get: P = 300 / 0.21 P = 14285.71

So, the sum of money is approximately ` 14285.71.