Question

Sum of two digit of digit number is eleven the original number is 9 more than the number after Interchanging the
digit.​

Answer 1

$\huge{\bf{\blue{\star{SOLUTION:-}}}}$

$\red{Let\: the\: digit\: at\: one's\: place= x }$

$\pink{Let\: digit\: at\: ten's\: place = y}$

$\blue{According\: to\: the\: question,}$

$\green{x + y = 11 ---- (eq.1)}$

$\red{Then,}$

$\orange{10y + x = 10x + y + 9}$

$\pink{9y - 9x = 9}$

$\blue{9(y - x ) = 9}$

$\red{y - x = 1 (eq.2)}$

$\green{eq.1 + eq.2}$

$\pink{x + y = 11}$

$\pink{+}$

$\pink{-x + y = 1}$

_____________

$\blue{2y = 12}$

_____________

$\green{y = 6}$

$\orange{ x = 11-6 = 5}$

______________

$<marquee>Thus, the number is 65</marquee>$

Answer 2

$\huge\mathfrak{Answer}$

65

$\huge\textsf{Explanation}$

Let the digits be x and y.

SO, the original number would be 10x + y (two digits numbers are of this form, when expanded)

Given, sum of digits = 11

⇒ x + y = 11

And, when the digits are interchanged, then the original number is 9 more than the new number.

So, ⇒ 10y + x + 9 = 10x + y

⇒ 9x - 9y = 9

⇒ 9(x - y) = 9

⇒ x - y = 9/9

⇒ x - y = 1

So, now we get that, x + y = 11 and x - y = 1

So, add these two equations to get the value of x

x + y + x - y = 11 + 1

⇒ 2x = 12

⇒ x = 6

Now, put the value of x in any equation to get the value of y.

⇒  x - y = 1

⇒ 6 - y = 1

⇒ - y = 1 - 6

⇒ - y = - 5

⇒ y = 5

So, the digits are 6 and 5, hence, the number would be :-

⇒ 10x + y

⇒ 10(6) + 5

⇒ 60 + 5

⇒ 65

Hence, the original number is 65.

$\rule{200}2$