The difference between simple interest on a certain sum at the annual rate of 12 percent for (3/2) years and (7/2) years is Rs. 1920. What is the sum?

Annual rate of interest (R) = 12%

Difference in time periods = $$\frac{7}{2}​$$​ years and $$\frac{3}{2}$$​ years

Difference in simple interest over these periods = Rs. 1920

​$$\text{Difference in SI} = \frac{P \times R \times (T_2 - T_1)}{100}$$​​

Substituting the values:

​$$1920 = \frac{P \times 12 \times \left(\frac{7}{2} - \frac{3}{2}\right)}{100}\\ \ \\1920 = \frac{P \times 12 \times 2}{100}\\ \ \\1920 = \frac{24P}{100}\\ \ \\1920 \times 100 = 24P \\ \ \\192000 = 24P \\ \ \\ P = \frac{192000}{24} = 8000$$​​

Thus, The sum is Rs. 8000.