Question

the sum of two digit number is 13 if this number is subtracted from the one obtained by interchanging the digits the result is 45 what is it number

Answer 1

Let the digits be x And y

given, x + y = 13

When writing a two digits number, we write

10x + y because they are in this form only.

So interchanging digits we get,

10y + x

given,

10y + x - (10x + y ) = 45

=> 10y + x - 10x - y = 45

=> 9y - 9x = 45

=> 9(y - x) = 45

=> y - x = 45/9

=> y - x = 5

Also given x + y = 13

adding these equations we get

x + y + y - x = 13 + 5

=> 2y = 18

=> y = 9

Since, x + y = 13

=> x + 9 = 13

=> x = 13 - 9

Hence, x = 4
So the digits is

10x + y = 49


Hope it helps dear friend ☺️✌️

Answer 2

$\large {\huge{ \color{green}{ \mathfrak{welcome}}}}$



$\large {\huge{ \color{red}{ \mathfrak{answer}}}}$



Let to be 10 unit digit number be x


then,

Let to be 1 unit digit number be y



Again......


$\bold{ \huge{ \fbox{x + y = 13}}}$




Now,


$\bold{ \huge{ \fbox{10x + 10y - 10y - x = 45}}}$

$\bold{ \small{ \fbox{9x - 9y = 45}}}$


$\bold{ \huge{ \fbox{9(x - y) = 45}}}$


$\bold{ \huge{ \fbox{x - y = \frac{45}{9}}}}$



$\bold{ \huge{ \fbox{x - y = 5}}}$



$\bold{ \huge{ \fbox{solving \: equation}}}$
we get


X=9


Y=4

$\bold{ \huge{ \fbox{now}}}$




$\bold{ \huge{ \fbox{10y + x}}}$


$\bold{ \huge{ \fbox{10(4) + 9}}}$


$\bold{ \huge{ \fbox{49}}}$



$\large {\huge{ \color{green}{ \mathfrak{dhanyavaad}}}}$