The sum of the digits in a two-digit number is 7. If you add 1 to each digit, you get a number

The sum of the digits in a two-digit number is 7. If you add 1 to each digit, you get a number that is 11 more than the specified number. What number is given?

Let the figure responsible for tens = X.

And the figure responsible for the units = U.

Then:

X + Y = 7;

Y = 7 – X.

The initial number can be written like this:

X * 10 + Y = X * 10 + 7 – X = 9 * X + 7.

The number formed by adding one to each digit can be written as follows:

(X + 1) * 10 + Y + 1 = 10 * X + 10 + 7 – X + 1 = 9 * X +18.

Their difference is 11:

9 * X + 18 – 9 * X – 7 = 11;

11 = 11.

This result suggests that there are many solutions, provided that:

Y = 7 – X.

Let’s check:

Let X = 2.

Y = 7 – 2 = 5.

The number is 25.

Adding 1 to each digit will give a new number: 36.

36 – 25 = 11.

All conditions are met.