5 years ago the average age of a family which includes father, mother and a son was 35 years. 3 years ago the average age of father and mother was 46 years. What is the present age (in years) of the son?

Options

A. 20
B. 24
C. 26
D. 22

Answer

To solve the problem step by step, we need to find the present age of the son based on the information given about the family ages.

### Step 1: Determine the total age of the family 5 years ago.
The average age of the family 5 years ago was 35 years. Since there are 3 members in the family (father, mother, and son), we can calculate the total age of the family 5 years ago.

\[ \text{Total age of family 5 years ago} = \text{Average age} \times \text{Number of family members} = 35 \times 3 = 105 \text{ years} \]

### Step 2: Calculate the total age of the family now.
Since 5 years have passed, we need to add 5 years for each family member to the total age calculated in Step 1.

\[ \text{Total age of family now} = \text{Total age 5 years ago} + (5 \times 3) = 105 + 15 = 120 \text{ years} \]

### Step 3: Determine the total age of the father and mother 3 years ago.
The average age of the father and mother 3 years ago was 46 years. Therefore, we can calculate their total age 3 years ago.

\[ \text{Total age of father and mother 3 years ago} = 46 \times 2 = 92 \text{ years} \]

### Step 4: Calculate the total age of the father and mother now.
Since 3 years have passed since the ages were calculated, we need to add 3 years for each parent.

\[ \text{Total age of father and mother now} = 92 + (3 \times 2) = 92 + 6 = 98 \text{ years} \]

### Step 5: Calculate the present age of the son.
Now we can find the present age of the son by subtracting the total age of the father and mother from the total age of the family.

\[ \text{Present age of son} = \text{Total age of family now} - \text{Total age of father and mother now} = 120 - 98 = 22 \text{ years} \]

### Final Answer:
The present age of the son is **22 years**.

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