x = 10, y = 20/6
Further explanation
Given
one number is three times of the other
their arithmetic mean is 10
Required
The numbers
Solution
Suppose the numbers you are looking for are x and y, then :
x = 3y (equation 1)
The arithmetic mean : the average of values
(x+3y)/2=10
x+3y = 20 (equation 2)
Substitute equation 1 into equation 2
3y+3y=20
6y=20
y = 20/6
from equation 1 :
x= 3 x 20/6
x = 60/6
x = 10