Becoming twice in the future: Twelve-year-old Sami is three times as old as his brother Vinay today. After how many years will Sami be exactly twice as old as Vinay, and what will Sami’s age be then?

Introduction / Context:We are given a current multiplicative relation and asked when a different multiplicative relation will hold in the future. Set up a single “t years from now” equation.

Given Data / Assumptions:

• Sami now = 12.
• Sami is 3 × Vinay ⇒ Vinay now = 4.
• Find t such that 12 + t = 2(4 + t).

Concept / Approach:Both ages grow by t; impose the “twice” relation at that future instant and solve for t, then compute Sami's age then.

Step-by-Step Solution:1) 12 + t = 8 + 2t.2) 4 = t.3) Sami's future age = 12 + 4 = 16.

Verification / Alternative check:Vinay will be 8 then; 16 = 2 × 8, confirming the condition.

Why Other Options Are Wrong:They are not the age at which the “twice” relation becomes true.

Common Pitfalls:Using 12 × 2 directly without shifting Vinay's age forward by t as well.

Final Answer:16 years