Question

A girls age is 2 times her sister. 4 years hence the product of their age is 160 find their ages

Answer 1

Answer:

Age of girl is 12 years and age of her sister is 6 years

Step-by-step explanation:

Let the age of sister be x years

Then the age of girl = 2x years

After 4 years

Age of sister = (x + 4) years

Age of girl = (2x + 4) years

Given that product of age is 160

Thus, we get

$(\,x + 4)\,(\,2x + 4)\, = 160\\\\2x^2 + 4x + 8x + 16 = 160\\\\2x^2 + 12x - 144\\\\ x^2 + 6x - 72 = 0\\\\x^2 + 12x - 6x - 72 = 0\\\\ (x +12)(x - 6)=0$

Either x = - 12 or x = 6

Since age can never be negative

Hence x = 6

Thus, age of sister = 6 years

Age of girl is 12 years

Answer 2

Let us assume that ,

The age of sister be " x "

Then , the age of girl will be " 2x "

After 4 years ,

The product of girl and her sister age is 160

Thus ,

⇒(x + 4) × (2x + 4) = 160

⇒2x² + 4x + 8x + 16 = 160

⇒x² + 2x + 4x + 8 = 80

⇒x² + 6x - 72 = 0

⇒x² + 12x - 6x - 72 = 0

⇒x(x + 12) - 6(x + 12) = 0

⇒(x - 6)(x + 12)

⇒x = 6 or x = -12 {Ignore the -ve value of x}

$\therefore \sf\underline{The \: age \: of \: girl \: and \: her \: sister \: are \: 12 \: and \: 6</p><p>}$