Question

If $a3b-ac=aa9$ then find $c-b-a$ if each of them is a distinctly different digit.

Answer 1

(i) Since the first digit of $\left(a3b\right)$ is written as it is after subtracting ac carry over from a to 3
(ii) There must be a carryover from 3 to b because if no carryover is there it means $3-a=a$
$\Rightarrow$ $2a=3$
$\Rightarrow$ $a=\frac{3}{2}$
Which is not possible because a is a digit For a carry over 1, 2 - a = a
$\Rightarrow$ $a=1$
(iii) it means $b$ and $c$ are the consecutive digit $(2,3),(3,4),.......(8,9)$