Out of 30 teachers of a school, a teacher of age 60 years retired. In his place another teacher of age 30 years was appointed. As a result, the mean age of the teachers will.
एक स्कूल के 30 शिक्षकों में से 60 वर्ष की आयु का एक शिक्षक सेवानिवृत्त हो गया। उसके स्थान पर 30 वर्ष की आयु के एक अन्य शिक्षक को नियुक्त किया गया। परिणामस्वरूप, शिक्षकों की माध्य आयु

Options

A. 2 वर्ष घट जाएगी
B. 6 माह घट जाएगी
C. 1 वर्ष घट जाएगी
D. उतनी ही रहेगी

Explanation

To solve the problem step by step, we will calculate the mean age of the teachers before and after the retirement and appointment of the new teacher.

### Step 1: Calculate the initial total age of the teachers.
Let the mean age of the 30 teachers be \( x \). Therefore, the total age of the 30 teachers can be calculated as:
\[ \text{Total Age} = \text{Mean Age} \times \text{Number of Teachers} = x \times 30 \]

### Step 2: Adjust the total age after the retirement of the 60-year-old teacher.
When the 60-year-old teacher retires, we subtract his age from the total age:
\[ \text{New Total Age} = x \times 30 - 60 \]

### Step 3: Add the age of the new teacher.
Now, we add the age of the new teacher (30 years) to the total age:
\[ \text{Final Total Age} = (x \times 30 - 60) + 30 = x \times 30 - 30 \]

### Step 4: Calculate the new mean age.
The number of teachers remains 30. Therefore, the new mean age can be calculated as:
\[ \text{New Mean Age} = \frac{\text{Final Total Age}}{\text{Number of Teachers}} = \frac{x \times 30 - 30}{30} = x - 1 \]

### Step 5: Conclusion about the change in mean age.
The new mean age is \( x - 1 \), which indicates that the mean age of the teachers has decreased by 1 year.

### Final Answer:
The mean age of the teachers will decrease by 1 year.

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