Parent–child ratio now and in the future: Deepak’s present age is three times that of his son. Five years hence, their ages will be in the ratio 34 : 13 (Deepak : Son). Find Deepak’s current age.

Introduction / Context:Another two-time ratio problem: represent present ages by a multiplier, shift both by the same future increment, and equate to the given future ratio. Solve for the multiplier and then compute the exact ages.

Given Data / Assumptions:

• If son = x, Deepak = 3x (present).
• After 5 years: (3x + 5) : (x + 5) = 34 : 13.

Concept / Approach:Convert the ratio into an equation and solve for x. Multiply as needed to recover Deepak’s age.

Step-by-Step Solution:1) (3x + 5) / (x + 5) = 34 / 13.2) Cross-multiply: 13(3x + 5) = 34(x + 5).3) 39x + 65 = 34x + 170 ⇒ 5x = 105 ⇒ x = 21.4) Deepak = 3x = 63 years.

Verification / Alternative check:Future ages: Deepak 68, son 26 → 68 : 26 = 34 : 13, confirming the condition.

Why Other Options Are Wrong:

• 58/60/68/54 do not produce the exact 34 : 13 ratio after 5 years when checked.

Common Pitfalls:Confusing which value the multiplier x represents or adding 5 to the ratio instead of the ages are frequent mistakes.

Final Answer:63 years