Father thrice son after 5 years; seven times 5 years ago: After five years the father will be three times the son’s age, and five years ago he was seven times the son’s age. Find the father’s current age.

Introduction / Context:
This classic age system uses two time-shifted multiplicative relations. Express both in terms of present ages, then solve simultaneously to find the father’s age. Because both relations are linear in the variables, straightforward substitution suffices.

Given Data / Assumptions:

• Let father's age be F and son's age be S (both present).
• F + 5 = 3(S + 5).
• F − 5 = 7(S − 5).

Concept / Approach:
Rearrange each equation to express F in terms of S and equate. Solve for S, then compute F. This avoids simultaneous elimination mistakes and keeps algebra transparent.

Step-by-Step Solution:

Verification / Alternative check:
Five years ago: 35 vs 5 (7×). In five years: 45 vs 15 (3×). Both conditions are satisfied.

Why Other Options Are Wrong:
35/45/50 do not satisfy both time-based multiplicative relations simultaneously.

Common Pitfalls:
Adding/subtracting years inconsistently between father and son, or mixing the 3× and 7× statements.

Final Answer:
40 years