Father three times son; sum after 10 years is 76: Shyam is 3 times as old as his son now. In 10 years, their ages will sum to 76. Find their present ages (father, son).

Introduction / Context:We combine a current multiplicative relation with a future sum. This yields a single linear equation in one variable (the son’s age), which can be solved directly and then scaled to get the father’s age.

Given Data / Assumptions:

• Let son = x; father = 3x.
• In 10 years: (x + 10) + (3x + 10) = 76.

Concept / Approach:Form the linear equation from the future sum and solve for x, then compute 3x. Age constraints (positive integers) are naturally met by the solution here.

Step-by-Step Solution:

Verification / Alternative check:In 10 years: son 24, father 52; 24 + 52 = 76 as required.

Why Other Options Are Wrong:39,13 or 45,15 do not satisfy the future-sum constraint when paired with the 3x relation.

Common Pitfalls:Adding 10 to only one person or mistaking “three times” for “three more than”.

Final Answer:42, 14