Question

When the digits of a two-digit number are interchanged, the new number becomes 39 less than 150% of the original number. If the sum of the digits is 6, find the original number.

Q: Answer-When the digits of a two-digit number are interchanged, the new number becomes 39 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 39 Multiplying both sides by 2, 20y 2x 30x 3y 78 28x 17y 78 . I And, x y 6 . II From II, x 6 y. Substitute in I 286 y 17y 78 168 45y 78 45y 90 y 2 Then x 6 2 4. So, original number 10 4 2 42.