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.

Answer 1

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)