The sum of the digits of a two-digit number is 9. When we interchange the digits it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?
Let the digits at tens place and ones place be x and (9−x) respectively.
Therefore, original number =10x+(9−x)=9x+9
On interchanging the digits, the digits at one's place and tens place will be x and (9−x) respectively.
Therefore, new number after interchanging the digits =10(9−x)+x
=90−10x+x
=90−9x
According to the given question,
New number = Original number +27
90−9x=9x+9+27
90−9x=9x+36
Transposing 9x to R.H.S and 36 to L.H.S, we obtain
90−36=18x
54=18x
Dividing both sides by 18, we obtain
3=x and 9−x=6
Hence, the digits at tens place and one's place of the number are 3 and 6 respectively.
Therefore, the two-digit number is 9x+9=9×3+9=36