The average age of the husband and wife at the time of their marriage 6 years ago was 28 years 6 months. Now the average of the husband, wife and a child is 24 years. How old is the child?

Options

A. `2 1/2` years
B. 3 years
C. `3 1/2` years
D. 4 years

Answer

To solve the problem, we will follow these steps:

### Step 1: Determine the current ages of the husband and wife.
The average age of the husband and wife at the time of their marriage 6 years ago was 28 years and 6 months.

First, we convert 28 years and 6 months into years:
- 6 months = 0.5 years
- Therefore, 28 years and 6 months = 28.5 years.

Since this was their average age 6 years ago, we can find their current average age:
- Current average age = 28.5 years + 6 years = 34.5 years.

### Step 2: Calculate the total current age of the husband and wife.
Since the average age of the husband and wife is 34.5 years, we can find their total age:
- Total age of husband and wife = Average age × Number of people
- Total age of husband and wife = 34.5 years × 2 = 69 years.

### Step 3: Determine the current average age of the husband, wife, and child.
We know that the average age of the husband, wife, and child is 24 years now.

### Step 4: Calculate the total age of the husband, wife, and child.
- Total age of husband, wife, and child = Average age × Number of people
- Total age of husband, wife, and child = 24 years × 3 = 72 years.

### Step 5: Find the age of the child.
Now we can find the age of the child by subtracting the total age of the husband and wife from the total age of the husband, wife, and child:
- Age of child = Total age of husband, wife, and child - Total age of husband and wife
- Age of child = 72 years - 69 years = 3 years.

### Conclusion:
The child is 3 years old.

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