The simple interest on a sum of money in 5 years at 12% per annum is Tk. 500 less than the simple interest accrued on the same sum in 7 years at 10% per annum. Find the sum.

Question: The simple interest on a sum of money in 5 years at 12% per annum is Tk. 500 less than the simple interest accrued on the same sum in 7 years at 10% per annum. Find the sum.

Solution:
Let the sum be P.
SI in 5 years at 12% per annum = P × 12 × (5/100) = 0.6 P
SI in 7 years at 10% per annum = P × 10 × (7/100) = 0.7 P

Now, according to the question,
0.7 P - 0.6 P = 500
⇒ 0.1 P = 500
⇒ P = 5000
Thus, the required sum is Tk. 5000