Question

sum of two digit number is 9.when we interchans the digits, it is found that the result new number is greater then the original number by 27. what is two digit number​

Answer 1

⌬ Let the Unit's place digit = M

⠀⠀⠀⌬ And the ten's place digit = N

⠀⠀⠀⌬ Then, Original Number = 10(M + N)

⠀⠀⠀⌬ Also, Interchaged Number = 10(N + M)

⠀

• F i r s t⠀C o n d i t i o n :

Sum of the two digits (M + N) number is 9.

$\begin{gathered}\twoheadrightarrow\sf M + N = 9 \qquad\quad\qquad\quad\Bigg\lgroup\sf eq^{n}\;(1)\Bigg\rgroup\\\\\end{gathered}$

• S e c o n d⠀C o n d i t i o n :

After Interchanging the digits, the new number is greater than the original number by 27.

$\begin{gathered}\longrightarrow\sf (10N + M) - (10M + N) = 27\\\\\\\end{gathered}$

$\begin{gathered}\longrightarrow\sf 9N - 9M = 27\\\\\\\end{gathered}$

$\begin{gathered}\longrightarrow\sf N - M = 3\\\\\\\end{gathered}$

$\begin{gathered}\longrightarrow\sf N = 3 + M \qquad\quad\qquad\quad\Bigg\lgroup\sf eq^{n}\;(2)\Bigg\rgroup\\\\\end{gathered}$

$\begin{gathered}\underline{\bigstar\:\sf{Substitue \: the \: value \: of \: N \: from \: eq^n \: (2) \: to \: eq^n \: (1) : }} \\ \\ \\ \end{gathered}$

$\begin{gathered}\longrightarrow\sf M + N = 9\\\\\\\end{gathered}$

$\begin{gathered}\longrightarrow\sf M + 3 + M = 9\\\\\\\end{gathered}$

$\begin{gathered}\longrightarrow\sf 2M = 9 - 3 \\\\\\\end{gathered}$

$\begin{gathered}\longrightarrow\sf 2M = 6 = 6/2 = 3 \\\\\\\end{gathered}$

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Answer 2

Step-by-step explanation:

S e c o n d⠀C o n d i t i o n :

After Interchanging the digits, the new number is greater than the original number by 27.

sum of two digit number is 9.when we interchans the digits, it is found that the result new number is greater then the original number by 27. what is two digit number