Average age of 4 daughters of a family is 8 years and average age of daughters along with their parents is 16 years. If mother is 4 years younger than father. Find the age of father 2 year ago.

The correct answer is 32 years.

Let us solve this problem step-by-step using average age concepts.

Step 1: Find the total age of the 4 daughters.
We are given that the average age of the 4 daughters is 8 years.

$\text{Total age of 4 daughters}=\text{Average age}\×\text{Number of daughters}$

$\text{Total age of 4 daughters}=8\×4=32\text{years}$

Step 2: Find the total age of all 6 family members (4 daughters + 2 parents).
The average age of the 4 daughters along with their parents (total 6 people) is 16 years.

$\text{Total age of 6 family members}=16\×6=96\text{years}$

Step 3: Find the combined age of the father and mother.
Subtract the total age of the 4 daughters from the total age of all 6 members:

$\text{Age of Father}+\text{Age of Mother}=96-32=64\text{years}$

Step 4: Find the present age of the father.
Let the father's present age be $F$ and the mother's present age be $M$.
We know that the mother is 4 years younger than the father:

$M=F-4$

Substitute $M$ into the combined age equation:

$F+(F-4)=64$

$2F-4=64$

$2F=68$

$F=34\text{years}$

So, the present age of the father is 34 years.

Step 5: Find the age of the father 2 years ago.
Subtract 2 years from the present age of the father:

$\text{Father's age 2 years ago}=34-2=32\text{years}$

Thus, the age of the father 2 years ago was 32 years.