Simple interest on an amount at 4% per annum for 13 months is more than the…

Step-by-Step Solution

To find the principal amount, we use the simple interest formula: Interest = (Principal * Rate * Time) / 100.

1. Define the variables:

   • Let the principal amount be P.

   • Case 1: Rate = 4% per annum, Time = 13 months = 13/12 years.

   • Interest 1 = (P * 4 * (13/12)) / 100 = (52P / 12) / 100 = 52P / 1200.

   • Case 2: Rate = 6% per annum, Time = 8 months = 8/12 years = 2/3 years.

   • Interest 2 = (P * 6 * (2/3)) / 100 = (12P / 3) / 100 = 4P / 100 = 48P / 1200.

2. Set up the equation:

   • The difference between the two interests is Rs. 40.

   • (52P / 1200) - (48P / 1200) = 40

   • 4P / 1200 = 40

3. Solve for P:

   • P / 300 = 40

   • P = 40 * 300

   • P = 12,000.