If a two digit number increases by 54 when the digits are reversed, what is the number?  

Expert Answers

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Let the digits of the number be x and y.

So we have

10*y + x  - (10*x + y) = 54

=> 10y + x – 10x – y = 54

=> 9y – 9x = 54

=> y – x = 54 / 9 = 6

=> y = 6 + x

Now, x can be 1, 2 or 3, it cannot take on higher values as that would make y a 2-digit number. The corresponding values of y for x equal to 1, 2 and 3 are 7, 8 and 9.

So the required number can be 17 , 28 and 39.

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