Question

the sum of two digit number is 9 if the digits are reversed the new number is 27 more than the original number find the original number ​

Answer 1

$\huge\mathfrak\blue{\underline{AnSwer:\:36}}$

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$\textbf{\underline{\underline{Step-By-Step\:Explanation:-}}}$

It is stated in the question that the sum of two - digit number is 9. And yeah! those numbers are unknown. So, first of all, Let the unknown number be ' PQ '

where ' P ' is in tens place and ' Q ' is in ones place.

Now,

$\sf\longrightarrow {P}+{Q}={9}$ _____________ ( ! )

From ( ! ), It can be said that $\sf\longrightarrow {Q}={9-P}$

It is stated that, when the digits are reversed, the new number is 27 more the the original number.

From this,

$\sf{10Q}+{P} = {10P} + {Q} + {27}$

$\sf\implies{10Q} + {9-Q} ={10}\times(9-Q) + Q + 27$

$\sf\implies{10Q}+{9-Q}={90}-{10Q}+Q+27$

$\sf\implies{18Q}={108}$

$\sf\implies Q=\dfrac{108}{18}$

$\sf\therefore {Q}=6$

So,

$\sf {P} + {Q}=9\\\\ \implies {P}+{6}=9\\\\ \implies {P}={9-6}\\\\ \implies {P}=3$

Hence,

$\textbf\orange{The\:original\:number\:is\:63}$

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$\huge\mathscr\green{Verification:}$

It is given in the question that the reverse of their numbers is 27 more than the original.

So,

63 - 36

= 27

Hence proved!

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