The simple interest on a certain sum of money at a certain rate of interest after 2.5 years is Rs.150 and the compound interest on the same sum of money at the same rate after 2 years is Rs.126. Find the difference between the compound interest and the simple interest on the same sum of money at the same rate after 3 years.

Let principal be P and rate be R%. SI for 2.5 years = P × R × 2.5 / 100 = 150, so PR = 150 × 100 / 2.5 = 6000. CI for 2 years at R% = P[(1 + R/100)² - 1] = 126. From PR = 6000, P = 6000/R. We need CI - SI after 3 years. CI₃ = P[(1 + R/100)³ - 1] and SI₃ = P × R × 3 / 100. The difference = P[(1 + R/100)³ - 1 - 3R/100]. Using CI₂ = P[(1 + R/100)² - 1] = 126 and solving gives R ≈ 6% and the difference ≈ 18.6. Option B is correct.