The average age of 5 siblings in a family is 10 years, whereas the average age of the siblings along with their parents is 18 years. If the mother is 6 years younger than the father, find the age of the father 3 years ago.

The correct option is 38 years.

Step 1: Calculate the total age of the 5 siblings.
Given that the average age of the 5 siblings is 10 years, the total age of the 5 siblings is:

$\text{Total age of 5 siblings}=5\times 10=50\text{years}$

Step 2: Calculate the total age of all 7 family members (5 siblings + 2 parents).
The average age of the 5 siblings together with their parents (total 7 people) is 18 years. Therefore, the total age of all 7 members is:

$\text{Total age of 7 members}=7\times 18=126\text{years}$

Step 3: Find the combined present age of the parents.
Subtracting the total age of the 5 siblings from the total age of all 7 family members gives the sum of the parents' present ages:

$\text{Age of Father}+\text{Age of Mother}=126-50=76\text{years}$

Step 4: Determine the father's present age.
Let the father's present age be $F$. Since the mother is 6 years younger than the father, her present age is $F-6$.
Substituting these into the equation for the sum of their ages:

$F+(F-6)=76$

$2F-6=76$

$2F=76+6=82$

$F=\frac{82}{2}=41\text{years}$

Step 5: Calculate the age of the father 3 years ago.
Subtracting 3 years from his present age:

$\text{Father's age 3 years ago}=41-3=38\text{years}$

Hence, the age of the father 3 years ago was 38 years.