Question

A number consists of 2 digit number whose sum is 9. If 27 is added to no.the digits are reversed then the number is ​

Answer 1

Answer:

36

Step-by-step explanation:

We know that the Sum of digits is 27

==> $x+y = 9$     ------- Eqn 1

Given that when 27 is added to the original number, the digits are reversed

Original number = $10x + y$

Final number = $10y + x$

==>$10x+y+27=10y+x$

==> $9y-9x=27$

Hence, y-x = 3 ------ Eqn 2

Adding Equations 1 and 2, we get:-

$y=6$

Hence,

$x=3$

Therefore, the number is:-

$10*3+6 = 36$

Answer 2

GIVEN :-

• Sum of the digits of a two digit number = 9

• If 27 is added to the number the digits are reversed .

TO FIND :-

• The two digit  number .

SOLUTION :-

   Let ,

   Digit in ten's place = x

   Digit in one's place = y

   Two digit number = 10x + y

    According to the first condition ,

    $\longrightarrow \sf x+y = 9 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .............................(1)$

    According to the second condition ,

   $\longrightarrow \sf 10x+y+27 = 10y+x \\\\\longrightarrow 10x-x+y-10y = -27 \\\\\longrightarrow 9x-9y = -27 \\\\\longrightarrow x-y = -3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .............................(2)$

   Add equation (1) and equation (2) ,

   $\longrightarrow\sf 2x = 6 \\\\\longrightarrow x= 3$

  Substitute x = 3 in equation (1) ,

  $\longrightarrow \sf 3+y = 9\\\\\longrightarrow y = 6$

  Two digit number = 36