Question

A number consists of two digits whose sum is $9$. If $9$ subtracted from the number, the digits interchange their places. Find the number.

Answer 1

Let the digits at ones place be x

Then the digits at tens place=9-x ......(sum of two digits is 9)

Therefore the number =10 (9-x)+x=90-10x+x=90-9x

Now,Number obtained by reversing the digits=10x+9-x=9x+9

It is given if 9 is subtracted from the number.,it's digits are interchanged.

90-9x-9=9x+9

81-9x=9x+9

81-9=9x+9x

18x=72

x=72/18

x=4

digits at ones place is x=4

tens place=9-x=9-4=5

Thus the number is 54