The difference between the compound interest and simple interest on a certain sum for 3 years at the same rate of interest is Rs. 248. Also, the simple interest on the same sum for 2 years at the same rate is Rs. 1600. Find the amount obtained at compound interest after 3 years.

Let the principal be P and rate be r% per annum. Given, simple interest for 2 years = Rs. 1600 So, (P x r x 2) / 100 = 1600 Pr / 100 = 800 ...(1) Now, Difference between CI and SI for 3 years = P(r/100)^2 (3 + r/100) We know from (1): Pr / 100 = 800 Try the standard rate value that satisfies the given difference. If r = 10%, then P x 10 / 100 = 800 P = 8000 Now check the difference: Difference between CI and SI for 3 years = P(r/100)^2 (3 + r/100) = 8000 x (10/100)^2 x (3 + 10/100) = 8000 x (1/100) x 3.1 = 80 x 3.1 = 248 This matches the given condition. So, Principal = Rs. 8000 Rate = 10% Amount after 3 years at CI: A = P(1 + r/100)^3 = 8000(1.1)^3 = 8000 x 1.331 = Rs. 10648 Hence, the correct answer is Rs. 10648.