Three years ago, the average age of a husband , wife and child was 26 years, and that of the wife and the child , 5 years ago, was 20 years . The present age of the husband is :

Options

A. A) 39 years
B. B) 42 years
C. C) 37 years
D. D) 45 years

Answer

To solve the problem, we will break it down step by step.

### Step 1: Understand the information given
Three years ago, the average age of the husband, wife, and child was 26 years. This means that the total age of the husband, wife, and child three years ago can be calculated as follows:

\[ \text{Average age} = \frac{\text{Total age}}{\text{Number of people}} \]
\[ 26 = \frac{\text{Total age (3 years ago)}}{3} \]

### Step 2: Calculate the total age three years ago
From the equation above, we can find the total age of the husband, wife, and child three years ago:

\[ \text{Total age (3 years ago)} = 26 \times 3 = 78 \text{ years} \]

### Step 3: Calculate their current total age
Since three years have passed, we need to add 3 years for each of the three individuals (husband, wife, and child) to find their current total age:

\[ \text{Current total age} = 78 + (3 \times 3) = 78 + 9 = 87 \text{ years} \]

### Step 4: Understand the second piece of information
We are also told that the average age of the wife and child five years ago was 20 years. We can set up a similar equation for the wife and child:

\[ 20 = \frac{\text{Total age (wife + child, 5 years ago)}}{2} \]

### Step 5: Calculate the total age of wife and child five years ago
From the equation above, we can find the total age of the wife and child five years ago:

\[ \text{Total age (wife + child, 5 years ago)} = 20 \times 2 = 40 \text{ years} \]

### Step 6: Calculate their current total age
Since five years have passed, we need to add 5 years for each of the wife and child (2 individuals) to find their current total age:

\[ \text{Current total age (wife + child)} = 40 + (5 \times 2) = 40 + 10 = 50 \text{ years} \]

### Step 7: Calculate the current age of the husband
Now we have the current total age of the husband, wife, and child (87 years) and the current total age of the wife and child (50 years). We can find the current age of the husband by subtracting the total age of the wife and child from the total age of the family:

\[ \text{Current age of husband} = \text{Current total age} - \text{Current total age (wife + child)} \]
\[ \text{Current age of husband} = 87 - 50 = 37 \text{ years} \]

### Final Answer
The present age of the husband is **37 years**.

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