Question

Q1.the number obtained by interchanging the digit of a 2-digit number is 9 more than the orignal number. if the sum of the digits is 9, than find the orignal number.​

Answer 1

Step-by-step explanation:

Given: The sum of the digits is 9. & The number obtained by Interchanging the digits of a two – digit number is 9 more than the Original number.

Need to find: The Original number?

⠀

❍ Let's consider that the two digits be x and y respectively.

Hence,

Original number = (10x + y).

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀

$\begin{gathered}:\implies\sf x + y = 9\\\\\end{gathered} </p><p></p><p>$

$\begin{gathered}:\implies\sf y = 9-x\qquad\quad\bigg \lgroup \frak Eq^n \;( \: I \: ) \bigg\rgroup\\\\\end{gathered} </p><p>$

$\begin{gathered}\underline{\bigstar\:{\pmb{\mathcal{ACCORDING\; \: TO\; \: THE\; QUESTION\; :}}}}\\\\\end{gathered} </p><p>$

The number obtained by Interchanging the digits of a two – digit number is 9 more than the Original number.

⠀

$\begin{gathered}\dashrightarrow\sf 10y + x = 10x + y + 9\\\\\end{gathered} </p><p>$

$\begin{gathered}\dashrightarrow\sf 9y = 9x + 9 \\\\\end{gathered} </p><p>$

$\begin{gathered}\dashrightarrow\sf y = x + 1\\\\\end{gathered} </p><p></p><p>$

$\begin{gathered}\dashrightarrow\sf x + 1 = 9-x\qquad\quad\bigg \lgroup\sf From\;eq^n \;( \: I \: ) \bigg\rgroup\\\\\end{gathered} </p><p>$

$\begin{gathered}\dashrightarrow\sf 2x = 8\\\\\end{gathered} </p><p></p><p>$

$\begin{gathered}\dashrightarrow\sf x = \cancel\dfrac{8}{2}\\\\\end{gathered} </p><p>$

$\begin{gathered}\dashrightarrow\underline{\boxed{\pmb{\frak{\pink{x =4}}}}}\:\bigstar\\\\\end{gathered} </p><p>$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀

$\begin{gathered}\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}\\\\\end{gathered} </p><p></p><p> </p><p> </p><p>$

⠀⠀⠀⠀

$\begin{gathered}\dashrightarrow\sf x + y = 9\\\\\end{gathered} </p><p>$

$\begin{gathered}\dashrightarrow\sf 4 + y = 9 \\\\\end{gathered} </p><p></p><p> </p><p>$

$\begin{gathered}\dashrightarrow\sf y = 9 - 4\\\\\end{gathered} </p><p></p><p>$

$\begin{gathered}\dashrightarrow\underline{\boxed{\pmb{\frak{\pink{y = 5}}}}}\;\bigstar\\\\\end{gathered} </p><p>$

✰ O r i g i n a l⠀N u m b e r :

⠀

$</p><p>\begin{gathered}\twoheadrightarrow\sf Number = 10x + y\\\\\end{gathered} </p><p></p><p>$

$\begin{gathered}\twoheadrightarrow\sf Numebr = 10\Big(4\Big) + 5\\\\\end{gathered} </p><p></p><p>$

↠Number=40+5

$\begin{gathered}\qquad\twoheadrightarrow\boxed{\boxed{\pmb{\frak{\purple{45}}}}}\:\bigstar\\\\\end{gathered} </p><p>$

Hence, the Original number is 45.