Question

sum of the digit of a two digit number is 9. the number obtain by reversing the digit of the given number by 27 find the number step by step explanation​

Answer 1

GIVEN:-

• Sum of the digit of a two digit number is 9.

• the number obtain by reversing the digit of the given number by 27.

TO FIND:-

• The Original Number .

Now,

$\implies\rm{One's\:digit\:be = x}$

$\implies\rm{ Ten's\:digit\:be = (x-9)}$

$\implies\rm{ Original\:Number = x + 10(9-x)}$

$\implies\rm{ Original\:Number =90- 9x}$

Now,

Atq.

$\implies\rm{ One's\:Digit = (x-9)}$

$\implies\rm{ Ten's\:Digit = (x)}$

$\implies\rm{ New\:Number = (9-x)+ 10(x)}$

$\implies\rm{New\:Number = 9- x + 10x}$

$\implies\rm{ New\:Number = 9x + 9}$

Therefore,

$\implies\rm{(New\:Number) - (Original\:Number) = 27}$

$\implies\rm{ (9x+9) - (90-9x) = 27}$

$\implies\rm{ 9x + 9 - 90 + 9x= 27}$

$\implies\rm{ 18x - 81 = 27}$

$\implies\rm{ 18x = 108}$

$\implies\rm{ x = \dfrac{108}{18}}$

$\implies\rm{ x = 6}$.

Thus,

Ones Digit = 6

Tens Digit = 9-6 = 3

Original Number = 36.

Answer 2

Answer with Step-by-step explanation:

Let the number be XY where X is in ten's place and Y is in unit place so it can also be written as 10(X)+Y. it is given that X+Y=9... Equation (1). It is also given that by reversing the order of digits of the number it increases by 27 so when it reverses Y is in ten's place and X is in unit place So the number becomes 10Y+X hence (10Y+X)-(10X+Y)=27=>9Y-9X=27=>Y-X =3... Equation (2). Add both equations then we get 2Y=12=>Y=6 => Substitute Y=6 in. equation (1) then X+6=9 =>X=3. Hence the number is 10(3)+6 =>36.

Hope it helps you...