Solve the following cryptarithmatic question
Find A,B,C,D,E,F
If,

A B
* B
______
B C

When A*B = 5

Dear student,

$$\begin{gathered} \mathrm{We} \mathrm{have}, \\ \mathrm{A}\times \mathrm{B}=5 \\ \Rightarrow \mathrm{A}=1 \mathrm{and} \mathrm{B}=5 \mathrm{or} \mathrm{A}=5 \mathrm{and} \mathrm{B}=1 \\ \mathrm{As}, \\ \mathrm{AB}\times \mathrm{B}\mathrm{BC} \\ \mathrm{If} \mathrm{A}=1 \mathrm{and} \mathrm{B}=5, \mathrm{then} \mathrm{AB}\times \mathrm{B}=15\times 5=75, \\ \mathrm{i}.\mathrm{e}. \mathrm{B}=7 \mathrm{and} \mathrm{C}=5, \mathrm{which} \mathrm{is} \mathrm{not} \mathrm{possible} \\ \mathrm{If} \mathrm{A}=5 \mathrm{and} \mathrm{B}=1, \mathrm{then} \mathrm{AB}\times \mathrm{B}=51\times 1=51, \\ \mathrm{i}.\mathrm{e}. \mathrm{B}=5 \mathrm{and} \mathrm{C}=1, \mathrm{which} \mathrm{again} \mathrm{is} \mathrm{not} \mathrm{possible} \\ \mathrm{So}, \mathrm{there} \mathrm{is} \mathrm{no} \mathrm{value} \mathrm{of} \mathrm{A} \mathrm{and} \mathrm{B} \mathrm{possible}. \end{gathered}$$

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