Sally is 5 years younger than the total of ages of Anna and Ruth.

Therefore, the sum of ages of the three girls is 5 years less than doubled sum of ages Ann and Ruth.


Hence, doubled age of Ann and Ruth is 41+5 = 46 years.


From here, the age of Ann and Ruth together is 46/2 = 23.


Anna is 3 years younger than Ruth. 


Hence, The doubled Anna age is 23-3 = 20 years.


From it,  the Ann age is 10 years.


ANSWER.  Ann is 10 years old.  Ruth is 23-10 = 13 years old. Sally's age is 10+13-5 = 18 years.


CHECK.  The total age of the three girls is  10 + 13 + 18 = 41 years.  ! correct !

PERSON           AGE
Anna             r-3
Ruth             r
Sally           (r-3)+r-5
TOTAL            41

Anna is 3 years younger than Ruth.  Sally is 5 years younger than the total of ages of Anna and Ruth.  The total of the ages of all the girls is 41.  Find the ages of the girls

Unlike the other person who responded, one ABSOLUTELY, UNEQUOVICALLY MUST state the variable being used, FIRST. 
In other words, you can't START out with r - 3 without stating FIRST, what "r" is. I've seen this many times, 
and it doesn't make any sense. I'm sure most, if not all folks, were taught about "Let statements."

Let Anna's age b A
Then Ruth's is: A + 3, and Sally's is A + A + 3 - 5, or 2A - 2
Since their ages sum to 41, we get: A + A + 3 + 2A - 2 = 41
                                                4A + 1 = 41
                                                    4A = 40
                                      Anna's age or 
You can now find the others' ages.