Question

The average age of 5 students is 18 years. If the teacher’s age is included, the average becomes 22 years. The teacher’s age is:

• A. 38 years
• B. 40 years
• C. 42 years
• D. 46 years

Hint:

Try the Deviation Method to solve this mentally! The teacher brings enough years to match the new average (22) AND increases the age of all 5 initial students by 4 years ($22 - 18 = 4$). $$\text{Teacher's Age} = \text{New Average} + (\text{Initial People} \times \text{Increase in Average})$$ $$\text{Teacher's Age} = 22 + (5 \times 4) = 22 + 20 = 42 \text{ years!}$$

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The average value represents a total quantity distributed equally among all individual constituents. When a new person enters a group and raises the group's collective average, it implies that the incoming person's value is higher than the original average. The change can be calculated by looking at the difference between the total sum of ages before and after adding the teacher.

Step 2: Key Formula or Approach:
1. $\text{Sum of values} = \text{Average} \times \text{Total number of individuals}$ 2. $\text{Teacher's Age} = \text{New Sum of Ages} - \text{Original Sum of Ages}$

Step 3: Detailed Explanation:
Let's find the total cumulative age values step-by-step: Initial State: There are 5 students with an average age of 18 years. \[ \text{Sum of 5 students' ages} = 5 \times 18 = 90 \text{ years} \] New State: The teacher joins the group, making the total number of individuals 6 ($5 \text{ students} + 1 \text{ teacher}$). This inclusion shifts the collective group average up to 22 years. \[ \text{New sum of ages (with teacher)} = 6 \times 22 = 132 \text{ years} \] Now, isolate the teacher's individual age by finding the difference between these two sum totals: \[ \text{Teacher's Age} = 132 - 90 = 42 \text{ years} \]

Step 4: Final Answer:
The age of the teacher is 42 years.