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Question -

A girl is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Find their present ages. [CBSE2010]



Answer -

Let age of sister = x years
Then age of girl = 2x years
4 years hence,
GirlтАЩs age = 2x + 4
and sisterтАЩs age = x + 4
According to the condition,
(2x + 4) (x + 4) = 160
=> 2x┬▓ + 8x + 4x + 16 = 160
=> 2x┬▓ + 12x + 16 тАУ 160 = 0
=> 2x┬▓+ 12x тАУ 144 = 0
=> x┬▓ + 6x тАУ 12 = 0
=> x┬▓ + 12x тАУ 6x тАУ 72 = 0
=> x (x + 12) тАУ 6 (x + 12) = 0
=> (x + 12) (x тАУ 6) = 0
Either x + 12 = 0, then x = тАУ 12 which is not possible being negative
or x тАУ 6 = 0, then x = 6
Age of sister = 6 years
and age of girl = 2x = 2 x 6 = 12 years

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