The average age of a husband and wife, who were married 7 years ago, was 25 years at the time of their marriage, Now, the average age of the family, including husband, wife and a child, born during the interval, is 22 years. What is the present age of the child?

Options

A. A)4 yrs
B. B)2 yrs
C. C)3 yrs
D. D)5 yrs

Answer

To solve the problem step by step, we will break down the information given and calculate the present age of the child.

### Step 1: Determine the present ages of the husband and wife.
- The average age of the husband and wife at the time of their marriage (7 years ago) was 25 years.
- Since the average age is calculated as the total age divided by the number of individuals, we can find the total age of the husband and wife at that time:
\[ \text{Total age at marriage} = \text{Average age} \times \text{Number of individuals} = 25 \times 2 = 50 \text{ years} \]

### Step 2: Calculate the present ages of the husband and wife.
- Since they were married 7 years ago, we need to add 7 years to their age at the time of marriage to find their current ages:
\[ \text{Present age of husband (H)} + \text{Present age of wife (W)} = 50 + 14 = 64 \text{ years} \]
(Here, we add 14 because both the husband and wife have aged 7 years each since their marriage.)

### Step 3: Calculate the total age of the family.
- The average age of the family (husband, wife, and child) is given as 22 years.
- To find the total age of the family, we multiply the average age by the number of family members:
\[ \text{Total age of family} = \text{Average age} \times \text{Number of family members} = 22 \times 3 = 66 \text{ years} \]

### Step 4: Find the present age of the child.
- We already calculated the total present age of the husband and wife to be 64 years. Now we can find the child's age by subtracting the total age of the husband and wife from the total age of the family:
\[ \text{Present age of child} = \text{Total age of family} - \text{Total age of husband and wife} = 66 - 64 = 2 \text{ years} \]

### Conclusion:
The present age of the child is **2 years**.

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