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.

$$\begin{array}{cc}\text{A=0}& \text{A=5}\\ IfA=0,4+B+A=B& IfA=5,A+A+B=B\\ \therefore 4+B=B& 10+B=B\\ Bcanonlybe0.& Bcanbeanythingfrom0to9except5\\ ButA=0;& Wehave1carryfor2ndcolumn\\ HenceBca{n}^{\prime }tbezero.Notwoletterscanrepresentsamedigits.& 1+4+B+A=B\\ & Carry10+B=B\\ & Similarly,for3rdcolumn\\ & 1+4+A=B\\ & Carry10=B\Rightarrow B=0\\ & \therefore A=5;B=0\\ & \end{array}$$