In each of the following cases, find the least value/values of letters used in place of digits :

$\begin{matrix} & & \text{A} & \text{B} \ & & \times & 5 \ \hline & \text{C} & \text{A} & \text{B} \ \hline \end{matrix}$

$\begin{matrix} & & \text{A} & \text{B} \ & & \times & 5 \ \hline & \text{C} & \text{A} & \text{B} \ \hline \end{matrix}$

Firstly, find the value of B.

$B \times 5 = B\\[1em] 0 \times 5 = 0\\[1em] 5 \times 5 = 25\\[1em]$

Possible values of B = 0 and 5.

Now, find the value of A

Lets take B = 0

$\begin{matrix} & & \text{A} & \text{0} \ & & \times & 5 \ \hline & \text{C} & \text{A} & \text{0} \ \hline \end{matrix}$

$A \times 5 = \text{CA}\\[1em] 5 \times 5 = 25\\[1em]$

Hence, A = 5 and C = 2

Now lets take B = 5

$\begin{matrix} & & \overset{2}{\text{A}} & \text{5} \ & & \times & 5 \ \hline & \text{C} & \text{A} & \text{5} \ \hline \end{matrix}$

$A \times 5 + 2 = CA$

No value for A satisfies this equation. Hence, B ≠ 5

$\begin{matrix} & & \text{5} & \text{0} \ & & \times & 5 \ \hline & \text{2} & \text{5} & \text{0} \ \hline \end{matrix}$

A = 5, B = 0 and C = 2