In an age problem, the father's present age is (x) years and the son's present age is (x-30) years. The product of their ages is 175. What is the father's present age?
Answer and explanation
Correct answer: 35 years
We have (x(x-30)=175), so (x^2-30x-175=0), which factors as ((x-35)(x+5)=0). Thus, (x=35) or (x=-5). Since an age cannot be negative, the father's age is 35 years. Option B would make the son's age (25-30=-5) years, so it is invalid. Exam tip: After solving an age equation, always reject roots that give a negative or otherwise unrealistic age.
Frequently asked questions
What is the correct answer to this question?
35 years
Why is this the correct answer?
We have (x(x-30)=175), so (x^2-30x-175=0), which factors as ((x-35)(x+5)=0). Thus, (x=35) or (x=-5). Since an age cannot be negative, the father's age is 35 years. Option B would make the son's age (25-30=-5) years, so it is invalid. Exam tip: After solving an age equation, always reject roots that give a negative or otherwise unrealistic age.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
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