If a certain sum of money becomes Rs. 7500 in 3.5 years and Rs. 11250 in 7 years at certain rate of interest at C.I. compounded annually. Then find the principal?

In compound interest, amounts after successive years form a geometric progression. If the amount after 3.5 years is Rs. 7500 and after 7 years is Rs. 11250, then the ratio A₇/A₃.₅ = 11250/7500 = 1.5. For a geometric progression with 3.5 year gap, this represents (1 + r/100)³·⁵ = 1.5. After 3.5 more years (7 years total), the factor would be 1.5² = 2.25. Working backwards: Principal = 7500/1.5 = 5000, which matches option C.