Question

A number consists of two digits whose sum is $9$. If $27$ is subtracted from the number its digits are reversed. Find the number.

Answer 1

Let the number $=ab=10a+b$

Sum of digits $=9$

$a+b=9$

number $-27$=number with reversrd digits

$10a+b-27=10b+a$

$9(a-b)=27$

$a-b=3$

$(a+b)+(a-b)=9+3\Rightarrow a=6,b=3$

$\therefore$ Required number is $63$