Question

When the digits of a two-digit number are interchanged, the new number becomes 19 less than 150% of the original number. If the sum of the digits is 11, find the original number.

Q: Answer-When the digits of a two-digit number are interchanged, the new number becomes 19 less than 150% of...

Let the unit digit and tens digit of the original number be y and x, respectively. Original number 10x y According to the data given 10y x 1.5 10x y 19 Multiplying both sides by 2, 20y 2x 30x 3y 38 28x 17y 38 . I And, x y 11 . II From II, x 11 y. Substitute in I 2811 y 17y 38 308 45y 38 45y 270 y 6 Then x 5. So, original number 10 5 6 56.