Question

the sum of the digits of a two digit number is 12 the number obtained by interchanging the two digits exceeds the given number by 18 find the number

Answer 1

$\text{If you observe any two digit number xy can be}\\\text{represented in the form }10x+y\\\text{If we interchange the digits we get yx or }10y+x\\\text{It is given that yx in greater than xy by 18 or}\\10y+x=10x+y+18\\\text{Rearranging we get,}\\9y=9x+18\\\Rightarrow y=x+2\\\text{It is also given that the sum of the digits is 12, So,}\\x+y=12\\\text{Put }y=x+2\\x+x+2=12\\\Rightarrow 2x=10\\x=5\\\text{Now, }y=x+2=5+2=7\\\text{Therefore, our number is 57.}$

Answer 2

Answer:

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