Question

.........heya.............
The sum of a two - digit number and the number obtained by reversing the digits of the number differ by 2 , find the number . how many such numbers are there ? ...
....plz solve with explanation....
Thanks ☺☺☺

Answer 1

Let the unit digit be X
ten 's digit be Y.
The original digit be ( X+10.Y)
now by reversing the digit we get (Y+10.x)

according to question

(X+10Y)+(Y+10X) = 66
11X+11Y = 66
11(X+Y) = 66
X+Y = 66/11
X+Y = 6 ------------------- 1eqn

hence digits differ by 2

So, X-Y = 2 ....................2eqn

Adding 1 and 2 equations we get

2X = 8
X = 8/2
so, X = 4

putting value of X in equation 1
X + Y = 6
4 + Y = 6
Y = 6 - 4
Y = 2

Therefore, number is given by putting value of X & Y

Hence, number is ( 4+10×2) = 24...

Answer 2

$\color{red}Thanks \: \: for \: \: \: \: asking \: \: this \: \: question \: dear$

$\color{red} NAMSKAR$



$\color{green} ACCORDING TO THE. QUESTION$

$\color{brown} REQUIRED. ANSWER$

Let to be 10'unit Digit Number


$\color{yellow}{x}$



Let to be 1 unit digit number
$\color{blue}y$

Then,



10x+y+10y+x=66



11x+11y=66



$\color{maroon} \: Here \: \\ \\ taking \: common \: 11$




11(x+y)=66



x+y=66/11



x+y=6



$\color{brown}{ - - Equation \: Second}$

$\color{pink}{Now}$



X+y=6

X-y=2

$\color{red}Solving \: this \: \\ equations \: by \: Elimination \: method$

x+y=6

x-y=2

_______
2y=4

y=4/2

y=2

$\color{green}{Now \: Putting \: \: the \: value \: of \: y \: in \: another \: Equation}$

X+y=6

x+2=6

x=6-2

x=4

$\color{indigo}{Again}$

$\color{blue}Original \: Number$

$\color{red}10y + x$

$\color{green}10 \times 2 + 4$

$\color{violet}{24}$

$\color{maroon}{THANK. YOU SO MUCH DEAR}$