Question

A no. consists of 2 digit no. whose sum is 9. if 27 is added to no. the digits are reversed then th eno. is

Answer 1

✬ Number = 36 ✬

Step-by-step explanation:

Given:

• Sum of digits of a two digit number is 9.
• After adding 27 to the number it's digits get reversed.

To Find:

• What is the number ?

Solution: Let the tens digit be x and units digit be y. Therefore,

➨ Number is 10x + y

➨ x + y = 9

➨ x = 9 – y

A/q

• Now after adding 27 digits gets reversed

$\implies{\rm }$ 10x + y + 27 = 10y + x

$\implies{\rm }$ 10x – x + 27 = 10y – y

$\implies{\rm }$ 9x + 27 = 9y

$\implies{\rm }$ 9x – 9y = – 27

$\implies{\rm }$ 9(x – y) = – 27

$\implies{\rm }$ x – y = – 27/9

$\implies{\rm }$ x – y = – 3

$\implies{\rm }$ 9 – y – y = – 3

$\implies{\rm }$ 9 + 3 = 2y

$\implies{\rm }$ 12 = 2y

$\implies{\rm }$ 6 = y

So,

➽ Unit digit of number is y = 6

➽ Tens digit of number is x = 9 – 6 = 3

Hence, the number is 10x + y = 10(3) + 6

➽ 36

Answer 2

QUESTION:-

✯ᴀ ɴᴏ. ᴄᴏɴsɪsᴛs ᴏғ 2 ᴅɪɢɪᴛ ɴᴏ. ᴡʜᴏsᴇ sᴜᴍ ɪs 9. ɪғ 27 ɪs ᴀᴅᴅᴇᴅ ᴛᴏ ɴᴏ. ᴛʜᴇ ᴅɪɢɪᴛs ᴀʀᴇ ʀᴇᴠᴇʀsᴇᴅ ᴛʜᴇɴ ᴛʜᴇ ɴUMBER. ɪs

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,

AFTER ADDING ,

27 DIGITS GETS REVERSED,

THEREFORE,

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

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

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

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

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

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

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

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

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

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

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

$\sf\implies 2y=12$

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

$\sf\implies y=6$

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

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

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

$\sf\therefore x=9-y$

$\sf\therefore x=9-6$

$\sf\implies x=3$

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

$\sf\therefore 10x+y$

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

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

$\large{\boxed{\sf{the\:number\:is\:36}}}$

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