Question

Find the difference between the sum and difference of the digits of a 2-digit number if the ratio
between the digits of the number is 1 : 2 and the difference between the 2-digit number and the
number obtained by interchanging the digits is 36.​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\green{\underline \bold{Given :}}$

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• Ratio between the digits of the number is 1 : 2

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• Difference between the 2-digit number and the number obtained by interchanging the digits is 36.

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$\red{\underline \bold{To \: Find:}}$

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• Difference between the sum and difference of the digits of a 2-digit number.

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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Suppose x & y two digits and the ratio b/w the digits of the number is 1:2

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Therefore, x : y = 1 : 2 [Given]

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So, y = 2x --------(1)

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Hence, y is in ten's position and x is in unit place.

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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$\purple\longrightarrow$ (10y + x) - (10x + y) = 36

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$\underline{\bold{\texttt{From equation (1) , we get y = 2x }}}$

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⇛ (10 × 2x + x ) - (10x + 2x) = 36

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⇛ (20x + x) - (12x) = 36

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⇛ 21x - 12x = 36

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⇛ 9x = 36

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⇛ x = 4 ---------(2)

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$\underline{\bold{\texttt{Now putting the value of x in equation (1)}}}$

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⇛ y = 2 × 4

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⇛ y = 8

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Sum and the difference of the digits of the number (x + y) & (x - y) respectively.

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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$\underline{\bold{\texttt{Difference between (x + y) \& (x - y)}}}$

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⇛ (y+ x) - (y - x) ---------(3)

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Putting the value of x = 4 & y = 8 in the above equation.

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We get,

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⇛ (8 + 4) - (8 - 4)

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⇛ 12 - 4

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⇛ 8

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Hence difference between the sum and difference of the digits of a 2-digit number is 8

$\rule{200}5$