A sum of 6000 is divided between two brothers such that the simple interest on the amount for 2 years at 5% per annum for elder brother is equal to the simple interest on the amount for 3 years at 10% per annum for younger brother. Find the ratio between the interest occurred by elder and younger brother when compounded annually while keeping the remaining parameters same?

Let elder brother get amount E and younger get amount Y, with E + Y = 6000. Simple interest equality: E × 5 × 2 = Y × 10 × 3, giving 10E = 30Y or E = 3Y. Substituting: 4Y = 6000, so Y = 1500, E = 4500. Compound interest for elder after 2 years at 5%: 4500(1.05)² - 4500 = 461.25. Compound interest for younger after 3 years at 10%: 1500(1.1)³ - 1500 = 496.5. Ratio = 461.25 : 496.5 = 615 : 662 after multiplying by 4/3.