Question

The sum of the digits of a two digit number is 7 .The number obtained by interchanging the digits exceed the original number by 27 .Find the number​

Answer 1

Answer:

Let the digit at ten's place be 7-X. So 25 is your answer!

Step-by-step explanation:

Hope thi helps

Answer 2

$\frak{Let}\begin{cases}\sf{\;\;The\;digit\;at\;one's\;place={\textsf{\textbf{y}}}}\\\sf{\;\;The\;digit\;at\;ten's\;place={\textsf{\textbf{x}}}}\end{cases}$

Therefore, the number = (10x + y)

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Given that,

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• The sum of the two digit number is 7.

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Therefore,

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$\begin{gathered}:\implies\sf{x+y=7}\\\\\\:\implies\sf{x=7-y}\qquad\qquad\bigg\lgroup\sf{eq^n\;1}\bigg\rgroup\end{gathered}$

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After interchanging the digits,

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• Number = (10y + x)

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$\underline{\bigstar\;\boldsymbol{According\;to\;the\;Question:}}$

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• The number obtained by interchanging the digits exceed the original number by 27.

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Therefore,

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$\begin{gathered}:\implies\sf{10y+x=10x+y+27}\\\\\\\\:\implies\sf{10y-y+x-10x=27}\\\\\\\\:\implies\sf{9y-9x=27}\\\\\\\\:\implies\sf{9\;(y-x)=27}\\\\\\\\:\implies\sf{y-x=\cancel{\dfrac{27}{9}}}\\\\\\\\:\implies\sf{y-x=3}\end{gathered}$

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$\qquad\qquad\footnotesize{\underline{\bf{\dag\;}\frak{Substituting\;value\;of\;x\;from\;eq^n\;1:}}}$

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$\begin{gathered}:\implies\sf{y-7-y=3}\\\\\\\\:\implies\sf{2y=3+7}\\\\\\\\:\implies\sf{2y=10}\\\\\\\\:\implies\sf{y=\cancel{\dfrac{10}{2}}}\\\\\\\\:\implies\underline{\boxed{\frak{\pink{y=5}}}}\;\bigstar\end{gathered}$

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$\qquad\qquad\footnotesize{\underline{\bf{\dag\;}\frak{Substituting\;value\;of\;y\;in\;eq^n\;1:}}}$

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$\begin{gathered}:\implies\sf{x=7-y}\\\\\\:\implies\sf{x=7-5}\\\\\\:\implies\underline{\boxed{\frak{\purple{x=2}}}}\;\bigstar\end{gathered}$

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$\therefore\;{\underline{\sf{Hence,\;the\;two\;digit\;number\;is\;{\textsf{\textbf{25}}}}.}}$⠀⠀⠀