Question

A girl is twice as old as her sister. four years hence, the product of their ages will be 160 find the present ages?

Answer 1

Let the girl be 'x' . And Let her sister be '2x'.
Therefore,
(2x+4)(x+4)=160
2x^2+8x+4x+16=160
2x^2+12x=160-16
2x^2+12x=144
2(x^2+6x)=144
X^2+6x=72
X^2+6x-72=0
X^2+12x-6x-72=0
X(x+12)-6(x+12)=0
(X-6)(x+12)
X=6
Or x=-12
Since age cannot be negative .
Therefore,
the girls present age is 6yrs and
Her sister's age is 12yrs.

Answer 2

Let the girl's sister's age be x

The girl's age = 4x

According to qn,

(x+4)(4x+4) = 160

=> 4x^2 + 4x + 16x + 16 = 160

=> 4x^2 +20x -160+16 = 0

=> 4x^2 +20x-144 = 0

=> 4(x^2 + 5x- 36) = 0

=> x^2 +5x -36 = 0/4 = 0

=> x^2 +9x -4x -36 = 0

=> x(x+9) -4 (x+9) = 0

=> (x-4)(x+9) = 0

When x -4 = 0

=> x = 4

When x+9 = 0

=> x = -9

As age can never be negative,

the correct value of x = 4

So,

The girl's sister's age = 4

The girl's age = 4 x 2 = 8

Hope it helped :-)

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