• # question_answer The sum of both digits of a two digit number is 7. If the digits of the number are interchanged, the number so formed is greater than the original number by 27. Find the original number. A)  25        B)         26   C)  27                    D)  28

Let the number be $\left( 10x+y \right)$ $\because$       $x+y=7$                                 ?(i) and $(10y+x)-(10x+y)=27$ $\Rightarrow$               $9y-9x=27$ $\Rightarrow$               $y-x=3$                       ?(ii) $\therefore$From Eqs. (i) and (ii), $x=2$ and                   $y=5$ $\therefore$Original number = 25