Radioactive decay follows first order kinetics, so the half-life is constant and each half-life reduces the remaining sample to half of its previous amount. The number of half-lives in 15 years is 15/5 = 3. After each half-life the surviving fraction is multiplied by one-half, so after three half-lives the fraction remaining is (1/2)^3 = 1/8, which equals 12.5 percent of the original sample. The option 50 percent corresponds to one half-life only. The option 25 percent corresponds to two half-lives. The option 6.25 percent would require four half-lives, or 20 years. The first order nature of nuclear decay, with its characteristic constant half-life, is highlighted in NCERT kinetics. Understanding radioactive decay kinetics in this way ties directly into the wider study of chemical kinetics, where the same reasoning recurs across many problems. Plausibility check: starting at 100 percent and halving three times gives 100 → 50 → 25 → 12.5 percent, confirming that 12.5 percent remains after 15 years.