The arithmetic mean of two numbers is 10.01. find the numbers if one of them is 5.5 times less than the other.

We know that
the arithmetic mean or average  is the sum of a collection of numbers divided by the number of numbers in the collection
so
Let
a> one number
b> second number
(a+b)/2=10.01> a+b=20.02> equation 1
a=5.5b> equation 2
substitute 2 in 1
5.5b+b=20.02> 6.5b=20.02> b=20.02/6.5> b=3.08
a=5.5*(3.08)> 16.94

the answer is
the two numbers are
3.08 and 16.94