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Question
A girls is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Find their present ages.
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Solution
Let the present age of girl be x years then, age of her sister x/2 years
Then, 4 years later, age of girl (x + 4) years and her sister’s age be `(x/2+4)Years`
Then according to question,
`(x+4)(x/2+4)=160`
(x + 4)(x + 8) = 160 x 2
x2 + 8x + 4x + 32 = 320
x2 + 12x + 32 - 320 = 0
x2 + 12x - 288 = 0
x2 - 12x + 24x - 288 = 0
x(x - 12) + 24(x - 12) = 0
(x - 12)(x + 24) = 0
So, either
x - 12 = 0
x = 12
Or
x + 24 = 0
x = -24
But the age never be negative
Therefore, when x = 12 then
`x/2=12/2=6`
Hence, the present age of girl be 12 years and her sister’s age be 6 years.
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