The simple interest on a certain sum of money for 3 years is 225 and the compound interest on the same sum at the same rate for 2 years is 153 then the principal invested is

Let principal = P, rate = r. Simple Interest for 3 years: P × r × 3 = 225, so Pr = 75. Compound Interest for 2 years: P(1 + r)² - P = 153. Using Pr = 75, we get: P(1 + 2r + r²) - P = 153, P(2r + r²) = 153. Substituting Pr = 75: 2(75) + 75r = 153, giving r = 3/75 = 1/25 = 4%. Therefore P = 75/(1/25) = 1875. Verification: SI = 1875 × 0.04 × 3 = 225 ✓, CI = 1875(1.04)² - 1875 = 153 ✓