A girl is twice old as her sister .four years hence the product of their ages will be 160 find their ages
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Answer:
12 and 6
Step-by-step explanation:
Let the present age of her sister be 'a' and hence the present age of that girl should be twice of a that is 2a.
After four year:
Age of girl = 2a + 4
Age of her sister = a + 4
Product of their ages = 160
= > ( 2a + 4 )( a + 4 ) = 160
= > 2( a + 2 )( a + 4 ) = 160
= > a^2 + 4a + 2a + 8 = 160/2 = 80
= > a^2 + 6a + 8 = 80
= > a^2 + 6a + 8 - 80 = 0
= > a^2 + 6a - 72 = 0
= > a^2 + ( 12 - 6 )a - 72 = 0
= > a^2 + 12a - 6a - 72 = 0
= > a( a + 12 ) - 6( a + 12 ) = 0
= > ( a + 12 )( a - 6 ) = 0
= > a = - 12 or 6
a cant be -ve, so a = 6
Hence, present age of
Girl = 2a = 2(6) = 12 year
Her sister = a = 6 year
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