Present ratio of ages is 2 : 3 (A : B). Five years hence, the ratio will be 3 : 4. What is A’s present age?
Verbal Reasoning
Problems on Ages
Difficulty: Medium
Choose an option
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A10 years
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B15 years
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C25 years
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DData inadequate
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ENone of these
Answer
Correct Answer: 10 years
Explanation
Introduction / Context:We are given present and future age ratios. Represent the present ages using a single parameter and impose the future ratio after adding 5 years to both ages. Solve for the parameter to find A’s age.
Given Data / Assumptions:
- Now: A : B = 2 : 3 ⇒ A = 2x, B = 3x.
- After 5 years: (A + 5) : (B + 5) = 3 : 4.
- Find A’s present age.
Concept / Approach:Use cross-multiplication on the future ratio to get a linear equation in x. Compute A = 2x.
Step-by-Step Solution:
(2x + 5)/(3x + 5) = 3/4 ⇒ 4(2x + 5) = 3(3x + 5).8x + 20 = 9x + 15 ⇒ x = 5 ⇒ A = 2x = 10.Verification / Alternative check:
After 5 years: A = 15, B = 20 ⇒ 15 : 20 = 3 : 4 ✔.Why Other Options Are Wrong:
15 or 25 correspond to different x values that fail the future ratio; “Data inadequate” is false.Common Pitfalls:
Using 2x : 3x directly as 3 : 4 without adding 5 years to both.Final Answer:10 years