The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is :

Options

A. 50 years
B. 40 years
C. 35 years
D. None of the options

Answer

To find the present age of the husband, we can break down the problem step by step.

### Step 1: Calculate the total age of the husband, wife, and child 3 years ago.
Given that the average age of the husband, wife, and child 3 years ago was 27 years, we can use the formula for average:

\[ \text{Average} = \frac{\text{Total Age}}{\text{Number of Members}} \]

Let \( H \) be the present age of the husband, \( W \) be the present age of the wife, and \( C \) be the present age of the child.

Three years ago, their ages would be \( H - 3 \), \( W - 3 \), and \( C - 3 \).

The average age 3 years ago is given as 27:

\[ \frac{(H - 3) + (W - 3) + (C - 3)}{3} = 27 \]

Multiplying both sides by 3 gives:

\[ (H - 3) + (W - 3) + (C - 3) = 81 \]

Simplifying this, we get:

\[ H + W + C - 9 = 81 \]

So,

\[ H + W + C = 90 \quad \text{(Equation 1)} \]

### Step 2: Calculate the total age of the wife and child 5 years ago.
We know that the average age of the wife and child 5 years ago was 20 years.

Thus, we can write:

\[ \frac{(W - 5) + (C - 5)}{2} = 20 \]

Multiplying both sides by 2 gives:

\[ (W - 5) + (C - 5) = 40 \]

Simplifying this, we have:

\[ W + C - 10 = 40 \]

So,

\[ W + C = 50 \quad \text{(Equation 2)} \]

### Step 3: Substitute Equation 2 into Equation 1.
Now we can substitute Equation 2 into Equation 1 to find the present age of the husband.

From Equation 1:

\[ H + W + C = 90 \]

Substituting \( W + C = 50 \) into this equation gives:

\[ H + 50 = 90 \]

### Step 4: Solve for the present age of the husband.
Now, solving for \( H \):

\[ H = 90 - 50 \]

\[ H = 40 \]

Thus, the present age of the husband is **40 years**.

### Summary of Steps:
1. Calculate total age of husband, wife, and child 3 years ago using average.
2. Calculate total age of wife and child 5 years ago using average.
3. Substitute the total age of wife and child into the total age of husband, wife, and child.
4. Solve for the present age of the husband.