The average age of Ram and his two children is 17 years and the average age of Ram's wife and the same children is 16 years. If the age of Ram is 33 years, the age of his wife is (In years):

Options

A. 31
B. 32
C. 35
D. 30

Answer

To find the age of Ram's wife, we can follow these steps:

### Step 1: Calculate the total age of Ram and his two children.
The average age of Ram and his two children is given as 17 years. Since there are three individuals (Ram and his two children), we can calculate their total age using the formula for average:

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

Rearranging this formula gives us:

\[ \text{Total Age} = \text{Average} \times \text{Number of Individuals} \]

Substituting the values:

\[ \text{Total Age of Ram and his two children} = 17 \times 3 = 51 \text{ years} \]

### Step 2: Determine the total age of the two children.
We know that Ram's age is 33 years. Therefore, we can find the total age of his two children by subtracting Ram's age from the total age calculated in Step 1:

\[ \text{Total Age of the two children} = \text{Total Age of Ram and his two children} - \text{Age of Ram} \]

Substituting the values:

\[ \text{Total Age of the two children} = 51 - 33 = 18 \text{ years} \]

### Step 3: Calculate the average age of the two children.
Now that we have the total age of the two children, we can find their average age:

\[ \text{Average Age of the two children} = \frac{\text{Total Age of the two children}}{\text{Number of Children}} = \frac{18}{2} = 9 \text{ years} \]

### Step 4: Calculate the total age of Ram's wife and the two children.
The average age of Ram's wife and the two children is given as 16 years. Using the same formula for average:

\[ \text{Total Age of Ram's wife and the two children} = \text{Average} \times \text{Number of Individuals} \]

Substituting the values:

\[ \text{Total Age of Ram's wife and the two children} = 16 \times 3 = 48 \text{ years} \]

### Step 5: Determine the age of Ram's wife.
Now, we can find the age of Ram's wife by subtracting the total age of the two children from the total age of Ram's wife and the two children:

\[ \text{Age of Ram's wife} = \text{Total Age of Ram's wife and the two children} - \text{Total Age of the two children} \]

Substituting the values:

\[ \text{Age of Ram's wife} = 48 - 18 = 30 \text{ years} \]

### Final Answer:
The age of Ram's wife is **30 years**.

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