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 age.

Answer 1

Let the girl's sister age be x
Given: girl is twice as old as her sister
Girl's age = 2x yrs

After 4 years the product of their ages will be 160 (given)

After 4 years:
Girl's age after 4 years= 2x+4
Sister age after 4 years = x+4

ATQ
(2x+4)( x +4) = 160
2x² +8x + 4x +16 = 160
2x² + 12x +16= 160
2x² + 12x +16 -160= 0
2x² + 12x - 144= 0
2(x² + 6x - 72)= 0
x² + 6x - 72 = 0
x² + 12x - 6x - 72= 0
x(x + 12) -6(x +12)= 0
(x + 12) (x -6)= 0
(x +12) = 0 or  (x -6)= 0

x = - 12 or x= 6

Age cannot be negative, so x = 6

Age of girls sister is = x = 6 years.
Age of girl = 2x = 2× 6= 12 years

Hence, the age of girl is 12 years and age of girl sister is 6 years.

HOPE THIS WILL HELP YOU..

Answer 2

here is the ans.............