<p>The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If now the mean age of the teachers in this school is 39 years, then the age (in years) of the newly appointed teacher is</p>
Step-by-Step Solution
Key Concept: Use the relationship: Total sum of ages = Mean × Number of people. When one person leaves and another joins, the change in total sum equals the difference in their ages, which causes the mean to change.
<p><strong>Step 1:</strong> Find initial total sum of ages.</p><p>Initial mean = 40 years, Number of teachers = 25</p><p>Initial total sum = 40 × 25 = 1000 years</p><p><strong>Step 2:</strong> Find new total sum of ages.</p><p>New mean = 39 years, Number of teachers = 25 (unchanged)</p><p>New total sum = 39 × 25 = 975 years</p><p><strong>Step 3:</strong> Find the age of newly appointed teacher.</p><p>Change in total sum = Retiring teacher's age − New teacher's age</p><p>1000 − 975 = 60 − Age of new teacher</p><p>25 = 60 − Age of new teacher</p><p>Age of new teacher = 60 − 25 = 35 years</p><p>∴ Answer: A (35 years)</p>
Correct Answer: A