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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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#### APPEARS IN

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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