If a two digit number is added with a 0 between the single digit and the ten digit number, the three digit number will be 90 more than the original number. This three digit number is exactly 7 times of the original number

If a two digit number is added with a 0 between the single digit and the ten digit number, the three digit number will be 90 more than the original number. This three digit number is exactly 7 times of the original number

Let the original number be x in tens of bits and Y in bits, then the original number = 10x + y
The new three digit number is x, ten digit number is 0, and one digit number is y. The new three digit number is 100x + y
According to the meaning of the title,
The number of three digits obtained is 90 times more than the original number
(100x+y) - (10x+y) = 90 ---> 90x = 90 ---> x=1
The three digit number is exactly seven times the original number
100x + y = 7 (10x + y) ---- because x = 1, the substitution is reduced to 100 + y = 70 + 7Y -- > y = 5
So the original number is 15

For a three digit number, the number on the tenth digit is 0, and the sum of the other two digits is 12. If you subtract 2 from the one digit number and add 1 to the hundred digit number, you will get three digits
Compared with the original three digit number, the three digit number obtained by the transposition of the hundred digit number and the single digit number is 100 less, so the original three digit number can be obtained.

507

Insert a 0 between the ten and the single digits of two numbers, and the two digits become three digits, which is exactly 9 times of the original two digits

The answer is 45
Let ten bits be x and one bit be y
100x+y=(10x+y)×9
Simplification
5x=4y

It is known that the sum of ten digits and one digit of a two digit number is 6. If a 0 is inserted between its ten digits and one digit, the three digit number obtained is 7 times of the original two digits. How many are the original two digits?

Let X be the number in ten and y be the number in one
x+y=6
100x+y=7（10x+y） 100x+y=70x+7y 30x=6y 5x=y
x=1 ,y=5
The original double-digit number was 15