Question

in a two digit number sum of the digits is 9. If the digits are reversed the number increases by 9
plz answer it fastly

Answer 1

let nos be x and y
x+y=9
and
10x+y+9=x+10y
y-x=1

hence adding both eqn
2y=10
y=5
x=4
no is 45

Answer 2

Let the digit in tens place be x and the digit at one's place is y.

Then, the original number is 10x + y    ------ (*)

Number formed by reversing the digits is 10y + x.  

Given that Sum of the digits is 9.

= > x + y = 9    -------- (1)

Given that if the digits are reversed the number increases by 9.

= > 10y + x = 10x + y + 9

= > 10y - y + x - 10x = 9

= > 9y - 9x = 9

= > 9x - 9y = -9

= > x - y = -1    ------ (2)

On solving (1) & (2), we get

= > x + y = 9

= > x - y = -1

    --------------

     2x = 8

        x = 4.

Substitute x = 4 in (1), we get

= > x + y = 9

= > 4 + y = 9

= > y = 5.

Substitute x = 4 and y = 5 in (*), we get

= > 10x + y

= > 10(4) + 5

= > 45.

Therefore, the number is 45.

Hope this helps!