28. Bob and Alice
Alice's age is the same as that of Bob if the digits are reversed. A year ago Alice was twice as old as Bob. How old are they?
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If Alices age is represented by the digits ab and Bob's by ba then the value of Alice's age is given by
10a + b
and Bob's age is
10b + a
Using these values, then one year ago we have
10a + b - 1 = 2(10b + a - 1)
so 10a + b - 1 = 20b + 2a - 2
and the only integer values (between 1 and 9) that satisfy this are a = 7 and b = 3. So Alice is 73 and Bob is 37.
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