How old are they?
Reversing the digits of grandfather Arthur's age gives that of his son Brain. The difference of their ages is three times that of Arthur's grandson Christopher, which in turn is a seventh of his grandfather's age . Neither Arthur nor Brian were teenage fathers. How old is Brain ? ( Hint: Arthur is more that 65 years old)
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1 solution
Let Arthur's age be 1 0 x + y for some digits x , y . Then Brian's age is 1 0 y + x , and the difference of their ages is 9 ( x − y ) . Let C be Christopher's age.
We are given 9 ( x − y ) = 3 C = 7 3 ( 1 0 x + y ) . Then 2 1 ( x − y ) = 1 0 x + y , so Arthur's age is a multiple of 21. We are given that he is older than 65, so he must be 8 4 . Then Brian is 4 8 . (and Christopher is 1 2 .)