Question

.A girl is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Find their present ages.

Answer 1

$\large\bf\underline{Given:-}$

• A girl is twice as old as her sister
• after Four years the product of their ages will be 160

$\large\bf\underline {To \: find:-}$

• Present ages of girl and her sister

$\huge\bf\underline{Solution:-}$

• Let present the age of sister be x years
• Present age of girl is 2x

≫ According to Question:-

Four years hence, the product of their ages (in years) will be 160.

After 4 years their ages :-

• Age of sister = 4 + x
• Age of girl = 2x + 4

»» (2x + 4) × (4 + x ) = 160

»» 2x(4 + x) +4(4 + x) = 160

»» 8x + 2x² + 16 + 4x = 160

»» 2x² + 12x = 160 -16

»» 2x² + 12x = 144

»» 2x² + 12x - 144 = 0

»» 2x² + 24x - 12x - 144

»» 2x (x + 12) - 12(x + 12)

»» (2x -12)(x + 12)

»» x = 12/2 or x = -12

»» x = 6 or x = - 12

✝️x is the age of girl's sister so age can't be negative so we will take x = 6 year's

hence

• present age of sister = 6 years
• Present age of sis 2x = 12 years .

$\rule{200}3$