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The Sum of the Ages of a Father and His Son is 45 Years. Five Years Ago, the Product of Their Ages (In Year) Was 124. Determine Their Presnet Ages. - ICSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

Question

The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages (in year) was 124. determine their presnet ages.

Solution

Let the present ages of father and his son be x years and (45 - x) years respectively.
Five years ago,
Father's age = (x - 5) years
Son's age = (45 - x - 5) years = (40 - x) years
From the given information, we have:

(x - 5) (40 - x) = 124
40x - x2 - 200 + 5x= 124
x2 - 45x + 324 = 0
x2 - 36x - 9x + 324 = 0
x(x - 36) - 9(x - 36) = 0
(x - 36) (x - 9) = 0
x = 36, 9
if x = 9,
Father's age = 9 years, Son's age = (45 - x) = 36 years
This is not possible
Hence, x = 36
Father's age = 36 years
Son's age = (45 - 36) years = 9 years

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Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Ex.6E | Q: 9
Solution The Sum of the Ages of a Father and His Son is 45 Years. Five Years Ago, the Product of Their Ages (In Year) Was 124. Determine Their Presnet Ages. Concept: Solutions of Quadratic Equations by Factorization.
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