Question

The average age of 14 students and their teacher is 20 years. If the teacher is excluded, then their average age reduces by 1.5 years. The teacher's age is:

• A. 41 years
• B. 30 years
• C. 39 years
• D. 59 years

Hint:

Use the deviation method to save time:
Teacher's age = Old Average + (Increase/Decrease in average $\times$ remaining number of people)
Teacher's age $= 20 + (1.5 \times 14) = 20 + 21 = 41$ years.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
This question requires us to determine the age of the teacher based on the change in the overall average age of the group when the teacher is excluded.

Step 2: Key Formula or Approach:
The sum of ages can be calculated using the formula:
\[ \text{Sum of ages} = \text{Average age} \times \text{Number of people} \]
We will find the total sum of ages before and after excluding the teacher, and subtract the latter from the former to get the teacher's age.

Step 3: Detailed Explanation:
Let us perform the calculations systematically:

• Initial Scenario:
Number of people = 14 students + 1 teacher = 15 people.
Average age = 20 years.
Sum of initial ages $= 15 \times 20 = 300$ years.

• Scenario after excluding the teacher:
Remaining number of people = 14 students.
New average age reduces by $1.5$ years, so New Average $= 20 - 1.5 = 18.5$ years.
Sum of ages of 14 students $= 14 \times 18.5 = 259$ years.

• Calculating the Teacher's Age:
Teacher's age = Sum of initial ages - Sum of students' ages
Teacher's age $= 300 - 259 = 41$ years.

Step 4: Final Answer:
The teacher's age is 41 years, which corresponds to option (A).