Question

$\begin{array}{cc}4A& \\ 4BA& \\ +AAB& \\ 1BBB& \end{array}$
A =___;

B=___

Answer 1

For A + A + B = B, A can be 0 or 5.

$\begin{array}{cc}\text{A=0}& \text{A=5}\\ \text{If A = 0, 4 + B +A = B}& \text{If A = 5, A + A + B = B}\\ \therefore \text{4 + B = B}& \text{10 + B = B}\\ \text{B can only be 0.}& \text{B can be anything from 0 to 9 except 5}\\ \text{But A = 0};& \text{We have 1 carry for 2nd column}\\ \text{Hence B can’t be zero.No two letters can represent same digits.}& \text{1 + 4 + B + A = B}\\ & \text{Carry 10 + B = B}\\ & \text{Similarly, for 3rd column}\\ & \text{1 + 4 + A = B}\\ & \text{Carry 10 = B ⇒ B = 0}\\ & \therefore \text{A = 5; B = 0}\\ & \end{array}$