Three friends Alan, Ben and Cal, the age of each of whom is a positive integer number of years, made the following statements in response to a query posited by Don, who is a mutual acquaintance. (It is known to Don that the age of each of the three friends exceeds 20 years.)
Alan: "If you take the two digits of my age and subtract 62, the result is 9 less than Ben's age."
Ben: "If you reverse the two digits of my age and subtract 12, the result is Cal's age with the digits reversed."
Cal: "If you reverse the two digits of my age and add 47, the result is Alan's age with the digits reversed."
Don was unable to determine their ages, and requested for additional clarification, when Alan replied, "If I tell you whether my age is prime or composite, you will be able to determine our ages."
Thereupon, Don accurately deduced their ages.
Determine the age of each of the three friends in conformity with the abovementioned statements.
Note: Don is a logician and math wizard.
It takes some time to ignore the red herrings introduced into
the scenario. Eliminating the reversal bla-bla D heard the following: <br><br>
A: I am less than 100 years old , and B is 53 yrs younger.
B: C is 21 years younger than I.
C: One more hint: 53+21=74. So, if you know my age- you
will know the rest. <br><br> good soul ,isn't he?
D (to himself): I now know the range of your ages : 21-25,42-46,95-99.
D ( loudly): I need one more hint...<br>
A: If I were to disclose whether my age is prime or composite
you would have no doubts about the right triplet.
D: OK, Pappa - you are 97. B is 44 . and C is 23.
D(to himself): Why did not C keep silent?, Was the digit reversal
by B time-consuming? Is it logical that they are "friends"?