A father's present age is 30 years more than his son's present age. After 5 years, the product of their ages will be 1375. What is the son's present age?
Answer and explanation
Correct answer: 20
Let the son's present age be \(x\) years. Then the father's present age is \(x+30\) years. After 5 years, their ages will be \(x+5\) and \(x+35\), respectively. Hence, \((x+5)(x+35)=1375\). For \(x=20\), the product is \(25\times55=1375\), so the son's present age is 20 years. The nearby distractor 25 is incorrect because it gives \(30\times60=1800\). Exam tip: in age problems, add the same number of years to both present ages when calculating their future ages.
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
Let the son's present age be \(x\) years. Then the father's present age is \(x+30\) years. After 5 years, their ages will be \(x+5\) and \(x+35\), respectively. Hence, \((x+5)(x+35)=1375\). For \(x=20\), the product is \(25\times55=1375\), so the son's present age is 20 years. The nearby distractor 25 is incorrect because it gives \(30\times60=1800\). Exam tip: in age problems, add the same number of years to both present ages when calculating their future ages.
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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