Father is 'three times more than' his son Ronit in age. After 8 years, he will be two and a half times Ronit's age. After a further 8 years, how many times Ronit's age will he be?

Problem restatementGiven a current multiplicative relation and a future relation (after 8 years), determine the multiplicative factor after another 8 years.

Given data & Assumption

• Interpretation note: The phrase “three times more than” is taken literally as four times as old (common in exam parlance), i.e., F = 4S. (If interpreted as “three times as old”, results differ; see Verification.)
• After 8 years: F + 8 = 2.5(S + 8).

Concept/ApproachUse two equations to solve present ages, then compute the ratio after a further 8 years.

Step-by-step calculation Let present ages be F (father), S (son). F = 4S F + 8 = 2.5(S + 8) 4S + 8 = 2.5S + 20 1.5S = 12 → S = 8,  F = 32 After a further 8 years (i.e., after 16 years total): F + 16 = 48,  S + 16 = 24 Required ratio = (F + 16)/(S + 16) = 48/24 = 2

Verification/AlternativeIf “three times more” were interpreted as “three times as old” (F = 3S), then 3S + 8 = 2.5(S + 8) gives S = 24, F = 72, and after 16 years the ratio would be 88/40 = 11/5 = 2.2. Because the prompt uses “more than”, many standardized questions expect the literal 4× reading, yielding a neat integer answer 2.

Common pitfalls

• Confusing “times more than” with “times as old”. Always check context and expected exam convention.
• Computing ratio after only 8 years instead of after a further 8 years (total +16).

Final Answer2 times