The average age of a husband and wife was 23 years when they were married 5 years ago. The average age of the husband , the wife and a child who was born during the interval , is 20 years now. How old is the child now ?

Options

A. 9 months
B. 1 years
C. 3 years
D. 4 years

Explanation

To solve the problem step by step, we need to analyze the information given in the question carefully.

### Step 1: Calculate the present age of the husband and wife.
When the husband and wife were married 5 years ago, their average age was 23 years. Therefore, we can calculate their total age at that time.

\[ \text{Total age of husband and wife 5 years ago} = \text{Average age} \times \text{Number of people} \]
\[ = 23 \times 2 = 46 \text{ years} \]

Now, since 5 years have passed, we need to add 5 years to each of their ages.

\[ \text{Present total age of husband and wife} = 46 + (5 \times 2) = 46 + 10 = 56 \text{ years} \]

### Step 2: Calculate the present average age of the husband, wife, and child.
We are given that the average age of the husband, wife, and child now is 20 years. Therefore, we can calculate their total age.

\[ \text{Total age of husband, wife, and child} = \text{Average age} \times \text{Number of people} \]
\[ = 20 \times 3 = 60 \text{ years} \]

### Step 3: Calculate the present age of the child.
Now we have the total age of the husband and wife, which is 56 years, and the total age of the husband, wife, and child, which is 60 years.

To find the age of the child, we subtract the total age of the husband and wife from the total age of the husband, wife, and child.

\[ \text{Present age of child} = \text{Total age of husband, wife, and child} - \text{Total age of husband and wife} \]
\[ = 60 - 56 = 4 \text{ years} \]

### Final Answer:
The child is currently **4 years old**.

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