A person's present age is \(x\) years. The product of the person's age 12 years from now and 12 years ago is 2160. What is the person's present age?
Answer and explanation
Correct answer: 48 years
According to the statement, \((x+12)(x-12)=2160\). Using the difference-of-squares identity, \(x^2-144=2160\), so \(x^2=2304=48^2\). Thus \(x=48\) or \(-48\), but age cannot be negative; hence the present age is 48 years. Check: \((48+12)(48-12)=60\times36=2160\). Exam tip: reject the negative root in age-based problems.
Frequently asked questions
What is the correct answer to this question?
48 years
Why is this the correct answer?
According to the statement, \((x+12)(x-12)=2160\). Using the difference-of-squares identity, \(x^2-144=2160\), so \(x^2=2304=48^2\). Thus \(x=48\) or \(-48\), but age cannot be negative; hence the present age is 48 years. Check: \((48+12)(48-12)=60\times36=2160\). Exam tip: reject the negative root in age-based problems.
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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