Question

Now answer my question

Answer 1

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$\underline{\blacksquare\:\:\:\footnotesize{\red{SolutioN}}}$

$\footnotesize{\text{Let , first place digit be = x}}$

$\footnotesize{\text{and , 2'nd place digit be = y}}$

$\therefore \:\:\footnotesize{\text{the original number is = 10y+x}}$

$\footnotesize{\text{and the reverse number is = 10x+y}}$

$\footnotesize{\text{and the reverse number is = 10x+y}}$

$\underline{\footnotesize{\text{According to the condition 1 :}}}$

$\footnotesize{\implies\:x-y=3\:\:.........(i)}$

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$\underline{\footnotesize{\text{According to the condition 2 :}}}$

$\footnotesize{\implies\:(10y+x)+(10x+y)=121\:}$

$\footnotesize{\implies\:10y+x+10x+y=121\:\:}$

$\footnotesize{\implies\:11y+11x=121\:\:}$

$\footnotesize{\implies\:11(x+y)=121\:\:}$

$\footnotesize{\implies\:(x+y)=\dfrac{\cancel{121}}{\cancel{11}}\:\:}$

$\footnotesize{\implies\:x+y=11\:\:...........(ii)}$

$\footnotesize{\text{from equation (i) and (ii) , doing [(i)+(ii)] , we get ;}}$

$\footnotesize{\implies\:x-y+x+y=3+11\:\:}$

$\footnotesize{\implies\:2x=14\:\:}$

$\footnotesize{\implies\:x=7\:\:}$

$\therefore\:\:\footnotesize{\:y=7-3=4\:\:}$

$\therefore\:\:\footnotesize{\text{the 2 digits number is = 74 or 47} }$

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