The simple interest on a sum of money in 5 years at 12 % per annum is Rs. 400 less than the simple interest accrued on the same sum in 7 years at 10 % per annum. Find the sum.

Sure, let's solve this step by step.

Step 1: Understand the problem We know that Simple Interest (SI) is calculated as (Principal (P) * Rate (R) * Time (T))/100. We are given that the SI for 5 years at 12% per annum is Rs. 400 less than the SI for 7 years at 10% per annum. We need to find the principal amount (P).

Step 2: Set up the equations Let's denote the principal amount as P. We can set up the following two equations based on the problem:

Equation 1: SI for 5 years at 12% per annum = (P * 12 * 5)/100 Equation 2: SI for 7 years at 10% per annum = (P * 10 * 7)/100

We also know from the problem that Equation 1 + Rs. 400 = Equation 2.

Step 3: Solve the equations Substitute Equation 1 and Equation 2 into the equation from Step 2:

(P * 12 * 5)/100 + 400 = (P * 10 * 7)/100

Simplify the equation:

60P + 40000 = 70P

Rearrange the equation to solve for P:

40000 = 10P

Finally, solve for P:

P = 40000 / 10 = Rs. 4000

So, the sum of money is Rs. 4000.