Question

the sum of the digits of a 2 digit number is 9.lf it is found that the resulting new number is greater than the original number by 27 what is the original number

anybody help me...​

Answer 1

Answer:

36

Step-by-step explanation:

let the ten's place digit be x.

let the unit's place digit be y.

therefore, the number is = (10x+y)

after swapping the two digits,

the  unit's place digit becomes x and the ten's place digit becomes y.

there, the new number is = (10y+x)

according to the question,

sum of the two digits is 9

i.e.

x + y = 9  --------- eqn. 1

again , the new number is greater than the original number by 27 , therefore we can say -

  (10y-x)-(10x-y)=27

⇒10y-x-10x+y=27

⇒9y-9x=27

⇒ (-9)(x-y)=9 x 3

⇒ x-y= -3 ------------ eqn. 2

solving eqn. 1 and eqn. 2 by elimination method :

x + y = 9

x - y =  -3

--------------

⇒2x= 6

⇒x=3

putting the value of x in eqn. 1 we get:

   x+y=9

⇒3+y=9

⇒y=9-3

⇒y=6

therefore the original number should be

=10x+y

putting the values of x and y

10x3 + 6 = 36