Question 438274
Let the 10s digit of Father's age = {{{a}}}
Let the units digit of Father's age = {{{b}}}
given:
Father's age = {{{10a + b }}}
Age of Son = {{{ 10b + a }}}
{{{ 10a + b - 1 = 2*( 10b + a - 1) }}}
{{{ 10a + b - 1 = 20b + 2a - 2 }}}
{{{ 8a = 19b - 1 }}}
This is 1 equation and 2 unknowns, so it's
not solvable directly.
I see that {{{ a > b }}}. I also see that the left 
side will always be even, so {{{b}}} must be 
odd for that to be.
So, {{{b}}} can be 3,5,7
 ({{{b}}} can't be {{{9}}}, since {{{ a>b }}}
{{{a}}} can be even or odd
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{{{ b = 7 }}}
{{{ 19b - 1 = 132 }}}
{{{8a}}} does not divide {{{132}}} for any {{{a}}}
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{{{ b = 5}}}
{{{ 19b - 1 = 94 }}}
{{{8a}}} does not divide {{{94}}}  for any {{{a}}}
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{{{ b = 3 }}}
{{{ 19b - 1 = 56 }}}
{{{ 8a = 56 }}}
{{{ a = 7}}}
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The father is 73 and the son is 37
check:
{{{ 10a + b - 1 = 2*( 10b + a - 1) }}}
{{{ 10*7 + 3 - 1 = 2*( 10*3 + 7 - 1) }}}
{{{ 70 + 2 = 2*( 30 + 6 ) }}}
{{{ 72 = 72 }}}
OK