A sum was put at simple interest at certain rate for 3 years. Had it been put at 3% lesser ratio,it would have fetch Rs.500 less.Find the sum.

Sure, let's solve this step by step.

Step 1: Understand the problem The problem is about simple interest. We know that the formula for simple interest is I = PRT/100, where P is the principal amount (the sum of money), R is the rate of interest, and T is the time in years.

Step 2: Set up the equations From the problem, we know that the interest earned was Rs.500 less when the rate was 3% less. So we can set up the following equations:

PRT/100 = I (this is the original interest) P(R-3)T/100 = I - 500 (this is the interest when the rate is 3% less)

Step 3: Solve the equations We can subtract the second equation from the first to get:

PRT/100 - P(R-3)T/100 = 500 PRT/100 - PRT/100 + 3PT/100 = 500 3PT/100 = 500

Step 4: Solve for P We know that T = 3 years, so we can substitute this into the equation to get:

3P*3/100 = 500 9P/100 = 500 P = 500 * 100 / 9 P = Rs. 5555.56

So, the sum of money that was put at simple interest was Rs. 5555.56.