9. The number ' $t u$ ' is the two-digit number with units digit $u$ and tens digit $t$. The digits $a$ and $b$ are distinct, and non-zero. What is the largest possible value of ' $a b$ ' - ' $b a$ ' ?
A 81
B 72
С 63
D 54
E 45
9. B First note that as ' $a b$ ' and ' $b a$ ' are two digit numbers, neither $a$ nor $b$ is equal to zero. Now ' $a b$ ' - ' $b a$ ' $=(10 a+b)-(10 b+a)=9 a-9 b=9(a-b)$. So for the difference to be as large as possible, $a$ must be as large as possible, that is 9 , and $b$ must be as small as possible, that is 1 .
So the required difference is $91-19=72$.