Question

The sum of the digits of a 2-digit no. is 8. The no. obtained by interchanging the digits exceeds the given no. by 18. Find the given nos.

Answer 1

10y+x=8

(10x+y) -(10y+x) =18

9x-9y=18

Divide by 9 on both sides

x-y=2

Answer 2

Original number

Tens Ones

8-x x

Now original no

=multiply by 1×x+multiply by10×(8-x)

=1×x+10×(8-x)

=x+80-10x

=-9x+80

Now after interchanging

New no is

Tens Ones

x 8-x

New no=multiply by1×(8-x)+multiply by 10×x

= 1×(8-x)+10×x

=8-1x+10x

=8+9x

Now we get original no= -9x+80

New no = 8+9x

Acc to ques

New no -( original no) =18

8+9x - (-9x+80) = 18

8+9x+9x-80 =18

18x = 18+72

18x=90

x=5

Now original no

Tens Ones

8-x x

=8-5 =5

=3 =5

Therefore original no is 35

New no

Tens Ones

x 8-x

=5 =8-5

=5 =3

Therefore New no after interchanging is 53

Hence original number is 35 and after interchanging is 53.

Thank you....