The sum of the digits of a 2-digit number is 11. If the digits are reversed, the number formed is 45 more than the original number. Find the original number. If x is the ten's digit and y is the one's digit, the original number is 10x+y. the number with reversed digits is 10y+x.

The original number is 38

Explanation:

Let the sum of the digits of a 2 digit number is 11.

If the digits are reversed, the number formed is 45 more than the original number.

Let x and y be the two numbers and

Let the original number be

Let the reversed number be

We need to determine the original number.

Original number:

We need to determine the original number

Thus, we have,

-----(1)

--------(2)

Solving the equation (2), we get,

                          --------(3)

Adding the equations (1) and (3), we get,

Thus, the value of x is 3

Substituting in equation (1), we get,

Thus, the value of y is 8.

The equation of the original number is

Substituting the value of x and y, we get,

Original number =

Thus, the original number is 38.

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