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Sagot :
Let the units place digit be U and the tens place digit be T.
The number N is given by:
[tex]N=10T+U\ldots(i)[/tex]The number K is given by:
[tex]K=10U+T\ldots(2)[/tex]It is given that N is even that means U can be only from 0,2,4,6,8.
It is also given that N exceeds K by more than 50 so it follows:
[tex]\begin{gathered} N-K\ge50 \\ 10T+U-(10U+T)\ge50 \\ 9T-9U\ge50 \end{gathered}[/tex]So it can be said that:
[tex]T-U\ge\frac{50}{9}\approx5.5556\approx6[/tex]Since the value of T-U will always be an integer and it should be greater than or equal to 6.
The number T can be 1 to 9 and U can be only 0,2,4,6,8 so it follows:
[tex]\begin{gathered} T=9,U=0\Rightarrow T-U=9 \\ T=9,U=2\Rightarrow T-U=7 \\ T=8,U=0\Rightarrow T-U=8 \\ T=7,U=0\Rightarrow T-U=7 \\ T=6,U=0\Rightarrow T-U=6 \\ T=8,U=2\Rightarrow T-U=6 \end{gathered}[/tex]Hence the possible values for integer N are 90,92,80,70,60,82 and the respective integer K will be 09,29,08,07,06,28.
In all cases the difference is more than 50 as you can check.
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