Analysis: If Liang Xiao is X years old this year, it is known that Grandma is 9 times as old as Liang Xiao this year, and Grandma is 9x years old this year;

Then, Xiao Liang was (x- 1) years old last year, and grandma was (9x- 1) years old last year.

Solution: Let Liang Xiao be x years old this year.

10 *(x- 1)= 9x- 1

10x- 10=9x- 1

x=9

Replace 9x=9 * 9 = 81,x-1= 9-1= 8,9x-1= 9 * 9-1= 80 with x = 9.

A: Xiao Liang is 9 years old this year and 8 years old last year; Grandma is 8 1 year old this year and 80 years old last year.