Question

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

Answer 1

SOLUTION :  

Let the age her sister be x years.

Girl's age be = 2x years

After four years :  

Her sister's age = (x + 4) years

Girl's age = (2x + 4) years

A.T.Q

Given 4 years later the product of their age will be 160

(x + 4) (2x + 4) = 160

2x² + 4x + 8x + 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

[By middle term splitting]

x(x + 12) - 6(x + 12) = 0

(x - 6) (x + 12) = 0

(x - 6) or  (x + 12) = 0

x = 6  or x = - 12  

Since, age can't be negative,x ≠ - 12 , Therefore, x = 6

Her sister's age = x = 6 years  

Girl's age = 2x = 2 × 6 = 12 years  

Hence, the present age of her sister be 6 years and girl age be 12 years .

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