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

difference between two numbers is 25

x - y = 25

the smaller one is 1/6th the larger

y = (1/6)x

by solving the system of equations

x - y = 25

y = (1/6)x

we find

x = 30

y = 5

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the numbers are 30 and 5.