If you give a three digit number, you can get a new number by transposing its hundred digit number and one digit number. The difference between the original number and the new book must be integer 9 and 11 Then divide the above. Please explain why?

If you give a three digit number, you can get a new number by transposing its hundred digit number and one digit number. The difference between the original number and the new book must be integer 9 and 11 Then divide the above. Please explain why?

Let the hundreds be x, the tens be y, and the bits be Z. if the original number is (100x + 10Y + Z), then the new number is (100z + 10Y + x). By subtracting the two numbers, we get 99x-99z = 99 (x-z). It can be divided by 9 and 11~

There is a two digit number, and the sum of the two digits is 9. If the number in one digit is transposed with the number in ten digit, the new two digits will be 63 larger than the original two digits,
Find the original two digits
Linear equation of one variable

Let a digit be X
10x+9-x=10(9-x)+x+63
9x+9=90-9x+63
18x=153-9
x=8
Ten digits: 9-8 = 1
This tree: 18