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.
Verbal Reasoning
Problems on Ages
Difficulty: Medium
Choose an option
-
A50 yr
-
B28 yr
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C42 yr
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D36 yr
Answer
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