Mother–daughter sum and a past 7× relation: The sum of a mother’s and daughter’s present ages is 50 years. Five years ago, the mother was 7 times the daughter’s age. Find their present ages (mother, daughter).
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A35 years, 15 years
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B38 years, 12 years
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C40 years, 10 years
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D42 years, 8 years
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ENone of these
Answer
Correct Answer: 40 years, 10 years
Explanation
Introduction / Context:Here we combine a sum constraint with a time-shifted multiplicative relation. Such problems resolve neatly via substitution after expressing one variable in terms of the other using the sum, then enforcing the past 7× condition.
Given Data / Assumptions:
- Let present mother age be M, daughter age be D.
- M + D = 50.
- Five years ago: M − 5 = 7(D − 5).
Concept / Approach:Use M = 50 − D in the second equation and solve for D. Then compute M. This ensures algebra is minimal and transparent.
Step-by-Step Solution:
(50 − D) − 5 = 7(D − 5)45 − D = 7D − 35 ⇒ 80 = 8D ⇒ D = 10M = 50 − 10 = 40Verification / Alternative check:Five years ago: 35 and 5 → 35 = 7 × 5; sum now 50; all constraints consistent.
Why Other Options Are Wrong:Other pairs fail the 7× relation or the sum-of-ages constraint.
Common Pitfalls:Mixing present and past values incorrectly; always subtract the same years from both individuals in past relations.
Final Answer:40 years, 10 years