A father's age is 28 years more than his son's age. After 4 years, the product of their ages will be 960. What is the son's present age?
Answer and explanation
Correct answer: 16
Let the son's present age be \(x\) years. The father's present age is then \(x+28\) years. After 4 years, their ages will be \(x+4\) and \(x+32\), respectively. Thus, \((x+4)(x+32)=960\), which gives \(x^2+36x-832=0\). Its positive solution is \(x=16\); the negative solution cannot represent an age. Check: after 4 years, the ages will be 20 and 48, and \(20\times48=960\). Exam tip: In age problems, reject any negative or otherwise unrealistic root.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
Let the son's present age be \(x\) years. The father's present age is then \(x+28\) years. After 4 years, their ages will be \(x+4\) and \(x+32\), respectively. Thus, \((x+4)(x+32)=960\), which gives \(x^2+36x-832=0\). Its positive solution is \(x=16\); the negative solution cannot represent an age. Check: after 4 years, the ages will be 20 and 48, and \(20\times48=960\). Exam tip: In age problems, reject any negative or otherwise unrealistic root.
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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