Question

A number consists of two digits whose sum is 8. If 18 is added to the
number its digits are reversed. Find the number.​

Answer 1

$\sf{Let \: one \: digit \: of \: the \: number \: be \: x , then \: it's \: ten} \:$

$\sf{digits \: will \: be \: (8 - x) }$

$\sf{So, given \: number = 10(8 - x) + x}$

$\sf{ = (80 - 10x + x)}$

$\sf{ = (80 - 9x)}$

$\sf{Now \: if \: digits \: are \: reserved , then \: number \: obtained} \:$

$\sf{= 10+(8-x)} \:$

$\sf{= 10x+8-x} \:$

$\sf{ = 9x+8} \:$

$\sf{Acc \: to \: question , } \:$

$\sf{(80-9x+18=9x+8)} \:$

$\sf{(98-9x=9x+8)} \:$

$\sf{90 = 18x} \:$

$\sf{x = 5} \:$

$\sf{⟹given \: number = 80 - 9x} \:$

$\sf{= 80-9 × 5} \:$

$\sf{ =80-45} \:$

$\sf{ =35} \:$

⟹ Hence , the number is 35.

Answer 2

Step-by-step explanation:

Let one digit of the number be x.

Then, its ten digit of the number be (8-x)

So, given number = 10(8-x) +x

➟ 80 - 10x + x

➟ 80 - 9x

Now, if digits are reversed,then number obtained:

➟ 10x + (8 - x)

➟ 10x + 8 - x

➟ 9x + 8

According to question,

➟ (80-9x) + 18 = 9x + 8

➟ 98 - 9x = 9x + 8

➟ 90 = 18x

➟ x = 5

Given number = 80 - 9x

➟ 80 - 9×5

➟ 80 - 45

➟ 35

∴ The number is 35.