Column equation:

[ 10×(x- 1)+x]×0.2 = x+(x- 1)

[ 10x- 10+x]×0.2 = x+x- 1

[9x- 10]×0.2=2x- 1

1.8x-2=2x- 1

2x- 1.8x=2- 1

0.2x= 1

x=5

x- 1=5- 1=4

This two-digit number is 45.