The sum of a two digit number and a ten digit number is 9. If the new number obtained by transposing the two digit number and a ten digit number is 9 larger than the original number, the original two digit number is () A. 54B. 27C. 72D. 45

The sum of a two digit number and a ten digit number is 9. If the new number obtained by transposing the two digit number and a ten digit number is 9 larger than the original number, the original two digit number is () A. 54B. 27C. 72D. 45

Let X be the one digit number of the original number, then the ten digit number is 9-x. according to the meaning of the question: 10x + (9-x) = 10 (9-x) + X + 9, the solution is: x = 5, 9-x = 4, then the original two digit number is 45

The sum of a two digit number and a ten digit number is 9. If the new number obtained by Jiang's transposition of a two digit number and a ten digit number is 9 larger than the original number, then the original two digit number is 9

Let the single digit be x and the ten digit be y
x+y=9
10y+x=10x+y-9
The solution is x = 5, y = 4
The original number was 45

For a two digit number, transpose the number in its ten digits with the number in its individual digits to get a new two digit number. Why can the difference between the original number minus the transposed number be divided by 9?

Suppose the single digit is a and the ten digit is B,
Then the two digits are 10B + a
The new double digits are 10A + B
（10b+a）-（10a+b）=9b-9a=9（b-a）
So it's always divisible by nine

For any three digit number, you can get a new number by subtracting its 100 digit number from its individual digit number. The difference between the original number and the new number can be divided by 9 and 11. Why

Suppose that the original three digits can be expressed as 100A + 10B + C, then the new three digits after the transposition of the hundred digit and the individual digit should be expressed as 100C + 10B + A. subtract the original three digits and the new three digits to get 99a-99c, and then write it as 99 (A-C), which can be divided by 9 and 11~