When 27 is added to a two digit number the result has the digits interchanged. What is the number?  

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Let the number consist of the digits x and y, or it is represented by xy. It is given that adding 27 to the number causes the digits to get interchanged:(xy + 27) = yx

We can write this as (10*x + y) + 27 = 10y + x

=>...

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Let the number consist of the digits x and y, or it is represented by xy. It is given that adding 27 to the number causes the digits to get interchanged:(xy + 27) = yx

We can write this as (10*x + y) + 27 = 10y + x

=> 10x + y  + 27 = 10y + x

=> 27 = 9y – 9x

=> 3 = y – x

=> y = 3 + x

To satisfy the relation y = 3 + x, x can take the values 1 , 2, 3 , 4, 5 and 6. y would be equal to 4 , 5, 6, 7 , 8 and 9

The required two digit number can be 14 , 25, 36, 47, 58 and 69

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