The present age of Sam is 24 years and the present age of Sam's mother is 48 years
Let the present age of Sam's mother = M
Let the present age of Sam = S
Sam's mother is twice as old as Sam so we can write
[tex]\rm M = 2S.........(1)\\[/tex]
12 years ago the age of Sam's mother = M - 12
After 12 years the age of Sam = S + 12
According to the given condition
[tex]\rm S + 12 = M-12 ......(2)[/tex]
From equations (1) and (2) solving for M and S we get
[tex]\rm S + 12 = 2S -12\\S = 24\\M = 2\times S = 2\times 24 = 48[/tex]
So we can conclude that the present age of Sam is 24 years and the present age of Sam's mother is 48 years.
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