Question

sum of the digit of a two digit number is 9 when we interchange the digit it is found that the resulting new number by 27, what is the two digit number​

Answer 1

Answer:

72

Step-by-step explanation:

sum is 9

let number be X and y

real number = 10x+y

so interchanged number = 10y+X

10y +X = 27

so, 10x+y = 72

Answer 2

${\tt{\red{\underline{\underline{\huge{Answer:- \: 36}}}}}}$

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$\LARGE{\bf{\underline{\underline\color{blue}{GIVEN:-}}}}$

• The sum of the two digits = 9

• On interchanging the digits, the resulting new number is greater than the original number by 27.

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$\LARGE{\bf{\underline{\underline\color{</strong><strong>purple</strong><strong>}{</strong><strong>Solution</strong><strong>:-}}}}$

Let us assume the digit of units place = x

Then the digit of tens place will be = (9 – x)

$\sf\green{Thus\: the\: two-digit\: number \: is \: 10(9 – x) + x }$

Let us reverse the digit

$\sf\green{The \: number \: becomes\: 10x + (9 – x) }$

$\begin{gathered}\begin{gathered}\underline{\boldsymbol{According\: to \:the\: Question :}} \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\: 10x + (9 – x) \: = \: 10(9 – x) + x + 27 }} }\\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \: 9x + 9 \: = \: 90 – 10x \:+ x + 27\\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \:9x + 9\: = \: 117 – 9x \\ \\ \\\end{gathered}\end{gathered}$

On rearranging the terms we get,

$\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \:18x \: = \: 108\\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\: x \: = \: 6}} }\\ \\\end{gathered}\end{gathered}$

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So the digit in units place = 6

Digit in tens place is

⇒ 9 – x

⇒ 9 – 6

⇒ 3

Hence the number is 36

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