Question

sum of the digits of a two-digit number is 9 .when we interchange the digit it is found that the resulting new number is greater than the original number by 27 .what is the two digit number​

Answer 1

Step-by-step explanation:

let the digits be x and y

A/Q

x+y=9 eq (I)

interchanging the digits

10y+x=10x+y+27

10y+x-10x-y=27

-9x+9y=27

9(x-y)=27

x-y=27/9

x-y=3. eq(ii)

x+y=9

x-y=3

2x=12

x=12/2

x=6

now,

x+y=9

6+y=9

y=9-6

y=3

therefore, the number will be

10x+y=10*6+3

=63 ans.

Answer 2

let the numbers be x and 9 - x

First no.= 10(x)+(9-x)

=10x-x+9

=9x+9

on interchanging

New no.=10(9-x)+x

=90-10x+x

=90-9x

so,

$9x + 9 - (90 - 9x) = 27 \\ 9x + 9 - 90 + 9x = 27 \\ 18x - 81 = 27 \\ 18x = 108 \\ x = 6$

No.=9x+9=54+9=63