What is the average age of children in the class ?
(i) Age of the teacher is as many years as the number of children.
(ii) Average age increased by 2 year if the teacher's age is also included.

Options

A. if the data in statement A alone is sufficient to answer the question
B. if the data in statement B alone is sufficient to answer the question.
C. if the data either in statement A alone or in statement B alone is
sufficient to answer the question
D. if the data given in both statements A and B together are not
sufficient to answer the question

Answer

To find the average age of children in the class based on the given statements, let's break down the information step by step.

### Step 1: Define Variables
Let:
- \( X \) = number of children in the class
- \( A \) = average age of children in the class
- \( T \) = age of the teacher

### Step 2: Analyze Statement (i)
From statement (i), we know:
- The age of the teacher is equal to the number of children, so:
\[ T = X \]

### Step 3: Analyze Statement (ii)
From statement (ii), we know:
- The average age increases by 2 years when the teacher's age is included. This can be expressed mathematically as:
\[ \frac{(A \cdot X) + T}{X + 1} = A + 2 \]
Substituting \( T \) from step 2:
\[ \frac{(A \cdot X) + X}{X + 1} = A + 2 \]

### Step 4: Simplify the Equation
Multiply both sides by \( (X + 1) \):
\[ (A \cdot X) + X = (A + 2)(X + 1) \]
Expanding the right side:
\[ (A \cdot X) + X = A \cdot X + 2X + A + 2 \]
Now, simplify by canceling \( A \cdot X \) from both sides:
\[ X = 2X + A + 2 \]
Rearranging gives:
\[ X - 2X = A + 2 \]
\[ -X = A + 2 \]
Thus:
\[ A = -X - 2 \]

### Step 5: Conclusion
The average age \( A \) of the children in the class is expressed in terms of \( X \):
\[ A = -X - 2 \]
Since \( A \) cannot be negative, this implies that we cannot determine a specific average age of the children based on the information given in both statements. Therefore, the data provided in both statements is insufficient to answer the question.

### Final Answer
The data given in both statements together are not sufficient to answer the question.

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