Let the two - digit number be xy (i.e. 10x + y).

After reversing the digits of the number xy, the new number becomes yx (i.e. 10y + x).

According to question -

(10x + y) = 4(x + y) + 3

⇒ 6x - 3y = 3

⇒ 2x - y = 1.....(1)

and,

(10x + y) + 18 = (10y + x)

⇒ 9x - 9y = - 18

⇒ x - y = - 2.....(2)

Subtracting equation (2) from (1), we get -

x = 3

Substitute the value of x in equation (1), we get -

y = 5

Thus, the required number is 35.