Question

A number consists of 2 digit number whose sum is 9. If 27 is added to no.the digits are reversed then the number is ​

Answer 1

Answer:

36

Step-by-step explanation:

The possibilities are 18,27,36,45.

18+27 not equal to 81

27+27not equal to 72

45+27 Not equal to 54

36+27 = 63

The number is 36

Answer 2

ANSWER✔

$\Large\underline\bold{GIVEN,}$

$\sf\dashrightarrow the\:sum\:of\:two\:digit\:number\:is\:9$

$\sf\dashrightarrow the\:digits\:get\:reverse\:when\:adding\:27\:to\:it$

$\Large\underline\bold{TO\:FIND,}$

$\sf\dashrightarrow THE\:NUMBER.$

$\sf\therefore \:taking\:two\:cases,$

$\sf\therefore in\:case1\:we\:will\:find\:the\:equation,$

$\sf\therefore getting\:reversed\:and\:finding \:the\:number$

$\Large\underline\bold{SOLUTION,}$

$\sf\therefore let\:the\:ten\:digit\:be\:x$

$\sf\therefore let\:the\:unit\:digit\:be\:y$

ACCORDING TO THE QUESTION,

$\large{\fbox {CASE:-1}}$

$\sf\therefore the\:equation\:we\:get\:is,$

$\sf\therefore 10x+y$

$\sf\therefore the\:sum\:of\:two\:digit\:number\:is\:9$

$\sf\therefore x+y=9$

$\sf\therefore x=9-y\:------eq^1$

$\sf{\boxed{\sf{x=9-y\:------eq^1}}}$

$\large {\fbox {CASE:-2}}$

$\sf\therefore the\:digits\:get\:reverse\:when\:adding\:27\:to\:it .$

ACCORDING TO GIVEN EQUATION,

AFTER ADDING ,

27 DIGITS GETS REVERSED,

$\sf\implies 10x + y + 27 = 10y + x$

$\sf\implies 10x - x + 27 = 10y - y$

$\sf\implies 9x + 27 = 9y$

$\sf\implies 9x -9y = - 27$

$\sf\implies 9(x - y) = - 27$

$\sf\implies x - y = \dfrac{-27}{9}$

$\sf\implies x - y = \cancel \dfrac{-27}{9}$

$\sf\implies x -y = - 3$

$\sf\implies 9 - y - y = - 3$

$\sf\implies 9-2y=-3$

$\sf\implies -2y=(-3)+(-9)$

$\sf\implies 2y=12$

$\sf\implies y = \dfrac{12}{2}$

$\sf\implies y=6$

$\sf {\fbox { y=6}}$

$\sf\therefore unit\:digit=6$

$\sf\therefore substituting\:the\:value\:of\:y\:in\:eq^1$

$\sf\therefore x=9-y$

$\sf\therefore x=9-6$

$\sf\implies x=3$

$\sf{\boxed{\sf{x=6}}}$

$\sf\therefore 10x+y$

$\sf\therefore equating\:values\:of\:x\:and\:y.\:we\:get,$

$\sf\therefore 10(3)+6$

$\large{\boxed{\sf{THE\:NUMBER\:IS\:36}}}$

$\large\underline\bold{THE\:NUMBER\:IS\:36.,}$

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