Question

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A two digit number is such that the product of its digit is 12 . When 36 is added to this number, the digits interchange their places. Find the number​

Answer 1

Answer:

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Answer 2

$\LARGE\textsf{\underline\textcolor{aqua}{↭ SoLuTioN :-}}$

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$\qquad\tt{:}\longrightarrow\large\textsf{Let the number at the units place be ' y ' }$

$\qquad\tt{:}\longrightarrow\large\textsf{Let the number at the tens place be ' x ' }$

$\qquad\tt{:}\longrightarrow\large\textsf{So the number formed will be ' 10x + y}$

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↭ According to the first condition we write the assumption :-

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$\qquad\tt{:}\longrightarrow\boxed{\large\textsf{xy = 12 -------- ( i )}}$

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↭ According to the second condition we write the assumption :-

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$\qquad\tt{:}\longrightarrow\large\textsf{10x + y + 36 = 10y + x}$

$\qquad\tt{:}\longrightarrow\large\textsf{10x - x + y - 10y + 36 = 0}$

$\qquad\tt{:}\longrightarrow\large\textsf{9x - 9y + 36 = 0}$

$\qquad\tt{:}\longrightarrow\large\textsf{x - y + 4 = 0 ------ ( Dividing by 9 on both the side's )}$

$\qquad\tt{:}\longrightarrow\boxed{\large\textsf{x = y - 4}}$

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↭ Substituting the value of ' x ' in the eq. ( i ) :-

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$\qquad\tt{:}\longrightarrow\large\textsf{( y - 4 )y = 12}$

$\qquad\tt{:}\longrightarrow\large\textsf{y² - 4y = 12}$

$\qquad\tt{:}\longrightarrow\large\textsf{y² - 4y - 12 = 0}$

$\qquad\tt{:}\longrightarrow\large\textsf{y² - 6y + 2y - 12 = 0}$

$\qquad\tt{:}\longrightarrow\large\textsf{y ( y - 6 ) + 2 ( y - 6 ) = 0}$

$\qquad\tt{:}\longrightarrow\large\textsf{( y + 2 )( y - 6 ) = 0}$

$\qquad\tt{:}\longrightarrow\boxed{\large\textsf{y = - 2 or y = 6}}$

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↭ As the given number can't be negative :-

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$\qquad\tt{:}\longrightarrow\boxed{\large\textsf\textcolor{red}{∴ The Value of y = 6}}$

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↭ Substituting the value of ' y ' in eq. ( i ) :-

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$\qquad\tt{:}\longrightarrow\large\textsf{6x = 12}$

$\qquad\tt{:}\longrightarrow\large\textsf{x = \cfrac{\large\textsf{12}}{\large\textsf{6}} }$

$\qquad\tt{:}\longrightarrow\boxed{\large\textsf\textcolor{red}{x = 2}}$

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$\qquad\boxed{\large\textsf\textcolor{orange}{∴ The number formed = 26 }}$

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