let 'x' and 'y' be the two numbers, and x>y

The difference between two numbers is 25

x - y = 25

The smaller number is 1/6th of the larger number

y = (1/6)x multiply both sides by 6

x = 6y

plug x = 6y into x - y = 25:

6y - y = 25

5y = 25 divide both sides by 5

y = 25/5

y = 5

the smaller number is 5.