Daughter’s present age from two conditions: Five years ago a mother was three times her daughter’s age. Five years from now the mother will be twice her daughter’s age. How old is the daughter today?
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A5 years
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B10 years
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C15 years
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D20 years
Answer
Correct Answer: 15 years
Explanation
Introduction / Context:Two time-shifted multiplicative relationships determine present ages uniquely. We solve a pair of linear equations derived from the English statements.
Given Data / Assumptions:
- M = mother's present age; D = daughter's present age.
- Five years ago: M − 5 = 3(D − 5).
- Five years from now: M + 5 = 2(D + 5).
Concept / Approach:Convert each to an equation in M and D, then eliminate M.
Step-by-Step Solution:1) From the first: M = 3D − 10.2) From the second: M = 2D + 5.3) Equate: 3D − 10 = 2D + 5 ⇒ D = 15.
Verification / Alternative check:Then M = 2D + 5 = 35. Check: Five years ago 30 vs 10 (3×); in five years 40 vs 20 (2×). Both hold.
Why Other Options Are Wrong:Other values fail one of the two conditions when verified.
Common Pitfalls:Arithmetic slips when moving constants: note −5 and +5 belong to both ages at the respective times.
Final Answer:15 years