Ages — scaling and future ratio (Anil and Purvi): At present Anil is 1.5 times Purvi’s age. Eight years hence, the ratio Anil:Purvi will be 25:18. Find Purvi’s present age.

Difficulty: Medium

Correct Answer: 28 yr

Explanation:


Introduction / Context:
Present multiplicative relation plus a future ratio gives two equations in one unknown (Purvi). Solve directly to find her current age.


Given Data / Assumptions:

  • A = 1.5P (present).
  • (A + 8) : (P + 8) = 25 : 18.


Concept / Approach:
Express Anil in terms of Purvi, substitute into the future ratio, and solve for P.


Step-by-Step Solution:

(1.5P + 8) / (P + 8) = 25 / 18.18(1.5P + 8) = 25(P + 8) ⇒ 27P + 144 = 25P + 200.2P = 56 ⇒ P = 28.


Verification / Alternative check:

Anil now = 1.5*28 = 42. After 8 years ⇒ 50 and 36 ⇒ ratio 50:36 = 25:18 ✓


Why Other Options Are Wrong:

  • 50, 42, 36 are not Purvi’s present age; they confuse the variables or time shift.


Common Pitfalls:

  • Using 1.5P as P/1.5 or swapping numerator/denominator in the ratio.


Final Answer:
28 yr

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