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Question
A girl is twice as old as her sister. Five years hence, the product of their ages (in years) will be 375. Find their present ages.
Solution
Let the age of the sister be “x”
The age of the girl = 2x
Five years hence
Age of the sister = x + 5
Age of the girl = 2x + 5
By the given condition
(x + 5) (2x + 5) = 375
2x2 + 5x + 10x + 25 = 375
2x2 + 15x – 350 = 0
a = 2, b = 15, c = – 350
x = `(-"b" ± sqrt("b"^2 - 4"ac"))/(2"a")`
= `(- 15 ± sqrt(225 - 4(2) (- 350)))/4`
= `(- 15 ± sqrt(225 + 2800))/4`
= `(- 15 ± sqrt(3025))/4`
= `(- 15 + 55)/4` or `(- 15 - 55)/4`
= `40/4` or `(-70)/4`
x = 10
Age will not be negative
Age of the girl = 10 years
Age of the sister = 20 years ...(2 × 10)
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