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Question

If an integer of two digits is k times the sum of its digits, the number formed by interchanging the digits is the sum of the digits multiplied by

Accepted Answer

Let n = 10a+b. The problem states that 10a+b=k(a+b). We want to find x, where 10b+a=x(a+b). Adding these two equations gives 11(a+b) = (k+x)(a+b). Because a+b 0, we have 11 = k + x, or x = 11-k.