Explanation:

Let $S$ be the current age of the son and $F$ be the current age of the father. **Condition 1: "The age of a father is two and a half times the age of his son."**\nThis can be written as an equation: $$ F = 2.5 \times S \\ F = \frac{5}{2} S \quad \text{(Equation 1)} $$ **Condition 2: "Five years ago, the father's age was thrice the age of the son then."**\nFive years ago: * Son's age was $S - 5$. * Father's age was $F - 5$. \nSo, the equation is: $$ F - 5 = 3 \times (S - 5) \quad \text{(Equation 2)} $$ \nNow, we substitute Equation 1 into Equation 2 to solve for $S$: $$ \left(\frac{5}{2} S\right) - 5 = 3(S - 5) $$\nDistribute the 3 on the right side: $$ \frac{5}{2} S - 5 = 3S - 15 $$\nTo eliminate the fraction, multiply the entire equation by 2: $$ 2 \times \left(\frac{5}{2} S\right) - 2 \times 5 = 2 \times (3S) - 2 \times 15 $$ $$ 5S - 10 = 6S - 30 $$\nNow, rearrange the terms to solve for $S$. Move $5S$ to the right side and $-30$ to the left side: $$ 30 - 10 = 6S - 5S $$ $$ 20 = S $$\nSo, the current age of the son is 20 years. **Verification:** * If the son's current age ($S$) is 20 years, then the father's current age ($F$) is $F = \frac{5}{2} \times 20 = 5 \times 10 = 50$ years. * Check Condition 1: Is 50 years two and a half times 20 years? Yes, $50 = 2.5 \times 20$. * Check Condition 2: Five years ago, son's age was $20 - 5 = 15$ years. Father's age was $50 - 5 = 45$ years. Is 45 years thrice 15 years? Yes, $45 = 3 \times 15$.\nBoth conditions are satisfied. \nLet's analyze why other options are incorrect: * **A. 15 years:** If $S=15$, then $F = 2.5 \times 15 = 37.5$. Five years ago, son was 10, father was 32.5. $32.5 \neq 3 \times 10$. * **B. 10 years:** If $S=10$, then $F = 2.5 \times 10 = 25$. Five years ago, son was 5, father was 20. $20 \neq 3 \times 5$. * **C. 12 years:** If $S=12$, then $F = 2.5 \times 12 = 30$. Five years ago, son was 7, father was 25. $25 \neq 3 \times 7$. \nThus, the correct age of the son now is 20 years.