The sum of the ages of a boy and his brother is 25 years, and the product of their ages in years is 126. Find their ages.

Let the present age of boy and his brother be x years and (25 – x) years

According to given question

x(25 – x) = 126

25x – x^{2} = 126

x^{2} – 25x + 126 = 0

Using the splitting middle term – the middle term of the general equation is divided in two such values that:

Product = a.c

For the given equation a = 1 b = – 25 c = 126

= 1.126 = 126

And either of their sum or difference = b

= – 25

Thus the two terms are – 18 and – 7

Sum = – 18 – 7 = – 25

Product = – 18. – 7 = 126

x^{2} – 18x – 7x + 126 = 0

x (x – 18) – 7(x – 18) = 0

(x – 18) (x – 7) = 0

x = 18 or x = 7

x = 18 (Present age of boy cannot be less than his brother)

if x = 18

The present age of boy is 18 years and his brother is (25 – 18) = 7years

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