Mother–son ages from past ratio and present sum – Eight years ago, Mrs. Lata was three times as old as her son. Their present ages total 64. How old is Mrs. Lata now?

Introduction / Context:We combine a past-time multiplier relation with a present-time sum. Writing both equations in terms of present ages prevents confusion and makes elimination straightforward.

Given Data / Assumptions:

• Let mother = M, son = S (present ages).
• Eight years ago: M − 8 = 3(S − 8).
• M + S = 64.

Concept / Approach:From M − 8 = 3S − 24 ⇒ M = 3S − 16. Substitute into M + S = 64 and solve for S; then compute M.

Step-by-Step Solution:M = 3S − 16.(3S − 16) + S = 64 ⇒ 4S = 80 ⇒ S = 20.M = 3 × 20 − 16 = 60 − 16 = 44.

Verification / Alternative check:Eight years ago: M − 8 = 36 and S − 8 = 12; 36 = 3 × 12, satisfied. Present sum: 44 + 20 = 64, satisfied.

Why Other Options Are Wrong:They fail either the 3× past relation or the present sum.

Common Pitfalls:Applying the factor 3 to present ages or forgetting to subtract 8 on both sides of the relation.

Final Answer:44