The sum of the ages of two friends is 40 years, and their product is 375 years². What is the age of the older friend?
Answer and explanation
Correct answer: 25 वर्ष
Let one friend’s age be \(x\) years. The other friend’s age is then \(40-x\) years. Thus, \(x(40-x)=375\), which gives \(x^2-40x+375=0\). Factoring, \((x-25)(x-15)=0\), so the two ages are 25 years and 15 years. Therefore, the older friend is 25 years old. Exam tip: In age problems, express the second age using the given sum and form a quadratic equation using the product.
Frequently asked questions
What is the correct answer to this question?
25 वर्ष
Why is this the correct answer?
Let one friend’s age be \(x\) years. The other friend’s age is then \(40-x\) years. Thus, \(x(40-x)=375\), which gives \(x^2-40x+375=0\). Factoring, \((x-25)(x-15)=0\), so the two ages are 25 years and 15 years. Therefore, the older friend is 25 years old. Exam tip: In age problems, express the second age using the given sum and form a quadratic equation using the product.
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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