The ratio of the present ages of a mother and daughter is 7 : 1. Four years ago, the ratio of their ages was 19 : 1. What will be the mother’s age four years from now?
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A42 years
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B38 years
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C46 years
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D36 years
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E48 years
Answer
Correct Answer: 46 years
Explanation
Introduction: Two time-separated ratios allow us to set up equations for present ages. With linear relationships, solve for the scale factor and compute the asked future age.
Given Data / Assumptions:
- Present: M : D = 7 : 1 → M = 7k, D = k.
- Four years ago: (M − 4) : (D − 4) = 19 : 1.
- We seek M + 4.
Concept / Approach: Substitute M and D into the past ratio and solve for k. Then compute the mother’s current age and add 4 years.
Step-by-Step Solution:
(7k − 4)/(k − 4) = 19 → cross-multiply.7k − 4 = 19k − 76 → 72 = 12k → k = 6.Mother’s present age M = 7k = 42; in 4 years → 46 years.Verification / Alternative check: Four years ago: Mother 38, Daughter 2 → ratio 38 : 2 = 19 : 1, correct.
Why Other Options Are Wrong: 42, 38, 36, 48 correspond to present or past ages or incorrect scaling; asked value is mother’s age 4 years hence.
Common Pitfalls: Using 4 years instead of subtracting 4 in the “four years ago” ratio or mixing present/future ages.
Final Answer: 46 years