Question

A girl is twice as old as her sister. Four years hence the product of their ages (in years)will be160. Find their present age.

Answer 1

LET, PRESENT AGE OF THE GIRL =2X
AGE OF HER SISTER =X
ACCORDING TO THE QUESTION
(2X+4)(X+4)=160
2X^2+8X+4X+16=160
2X^2+12X-144=0
2X^2+(24-12)X-144=0
2X(X+12)-12(X+12)=0
(2X-12)(X+12)=0
X=6;X=-12
(NEGLECT NEGATIVE VALUES)
SO ,AGE OF GIRL=12
AGE OF SISTER=6

Answer 2

Solutions :-

Let the age her sister be x
Girl's age = 2x

After four years,
Her sister's age = x + 4
Girl's age = 2x + 4

Product of their age = 160 years


According to the question,

=> (x + 4) (2x + 4) = 160
=> x (2x + 4) + 4(2x + 4) = 160
=> 2x² + 4x + 8x + 16 = 160

Now divide each term by 2. We get,
=> x² + 2x + 4x + 8 = 80
=> x² + 6x + 8 - 80 = 0
=> x² + 6x - 72 = 0
=> x² + (12 - 6)x - 72 = 0
=> x² + 12x - 6x - 72 = 0
=> x(x + 12) - 6(x + 12) = 0
=> (x - 6) (x + 12) = 0
=> x = 6, - 12 (Age always taken positively)


Hence,
Sister's age = x = 6 years
Girl's age = 2x = 2 × 6 = 12 years

_______________________

✯ @shivamsinghamrajput ✯