Question 680872
Note that the difference in their ages, which is
{{{ 41 - 14 = 27 }}}, will always stay the same
in the future.
I can express mom's future age as 
{{{ 10a + b }}}
and, Joan's age as 
{{{ 10b + a }}}
So, I have
{{{ 10a + b - ( 10b + a ) = 27 }}}
{{{ 10a + b - 10b - a = 27 }}}
{{{ 9a - 9b = 27 }}}
{{{ a - b = 3 }}}
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This is true now for Mom, since
{{{ 4 - 1 = 3 }}}
note tyhat
{{{ 5 - 2 = 3 }}}
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Mom will be 52 and Joan is 25 when digits are swapped
Note that {{{ 52 - 25 = 27 }}} as it should be
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The next time would be when
Mom is 63 and Joan is 36
{{{ 63 - 36 = 27 }}}