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?

Answer

To solve the problem step by step, we will break it down into manageable parts:

### Step 1: Determine the present ages of the husband and wife
The average age of the husband and wife when they were married 5 years ago was 23 years.

Let:
- Present age of the husband = A
- Present age of the wife = B

5 years ago, their ages would have been:
- Husband's age = A - 5
- Wife's age = B - 5

The average age at that time was given as 23 years. Therefore, we can set up the equation:

\[ \frac{(A - 5) + (B - 5)}{2} = 23 \]

### Step 2: Simplify the equation
Multiply both sides by 2 to eliminate the fraction:

\[ (A - 5) + (B - 5) = 46 \]

This simplifies to:

\[ A + B - 10 = 46 \]

Adding 10 to both sides gives:

\[ A + B = 56 \]

### Step 3: Determine the average age of the husband, wife, and child now
Now, we know that the average age of the husband, wife, and their child (who was born during the interval) is 20 years now.

Let:
- Present age of the child = C

The average age of the three individuals is given by:

\[ \frac{A + B + C}{3} = 20 \]

### Step 4: Simplify this equation
Multiply both sides by 3:

\[ A + B + C = 60 \]

### Step 5: Substitute the value of A + B
From Step 2, we know that \(A + B = 56\). We can substitute this into the equation from Step 4:

\[ 56 + C = 60 \]

### Step 6: Solve for C
Now, subtract 56 from both sides:

\[ C = 60 - 56 \]

This gives us:

\[ C = 4 \]

### Conclusion
The present age of the child is **4 years**.

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