Question

sum of digits of a two digit number is 9 . the number obtained by interchanging the digits exceeds the given number by 27 .find the orgin

Answer 1

Hey there !

Solution:

Let the digits be x and y

x + y = 9

=> x = 9 - y    = ( Equation 1 )

Original Number = 10x + y

Reversed Number = 10y + x

It is given that, Original number is less than the reversed number by 27.

=> 10x + y = 10y + x - 27

=> 10x - x + y - 10y = - 27

=> 9x - 9y = -27

Substituting x = 9 - y from equation 1 we get,

=> 9 ( 9 - y ) - 9y = -27

=> 81 - 9y - 9y = -27

=> 81 - 18y = -27

=> 81 + 27 = 18y

=> 108 = 18y

=> y = 108 / 18 = 6

Hence y = 6. Hence x = 9 - y, which is 9 - 6 which is 3

Hence x = 3 ; y = 6

Original Number = 10x + y

=> Original Number = 10 ( 3 ) + 6 = 30 + 6 = 36

Hence the original number is 36.

Hope my answer helped !

Answer 2

$\huge \boxed{ \mathbb{ANSWER:}}$


$<b> <I>$


→ Let the ten's digit of required number be x.
and, the unit's digit be y. Then,



=> x + y = 9.............(1).


→ Required number = ( 10x + y ).

→ Number obtained on reversing the digits = ( 10y + x ).


▶Now,

A/Q.

=> ( 10y + x ) - ( 10x + y ) = 27.

=> -9x + 9y = 27.

=> 9 ( -x + y ) = 27.

=> -x + y = 27/9.

=> -x + y = 3...............(2).



On adding equation (1) and (2), we get

x + y = 9.
-x + y = 3.
(-)..(+)...(+)
_______

=> 2y = 12.

=> y = 12/2.

=> y = 6.


➡ Putting y = 6 in equation (1), we get

=> x + 6 = 9.

=> x = 9 - 6.

=> x = 3.


Thus, the required number = 10x + y.

= 10 × 3 + 6.

$\huge \boxed{= 36.}$


$<marquee> <u> ✔✔ Hence, the required number is founded ✅✅.$

____________________________________
$</marquee></b></I></u>$



$\huge \boxed{ \mathbb{THANKS}}$



$\huge \bf{ \#BeBrainly.}$