Question

Average age of 29 students in a class is 14 when the age of the teacher is also included the average increased by 1 then what is the age of teacher ?

• A. 44
• B. 25
• C. 65
• D. 54

Answer 1

Answer:

A. 44

Understanding the Concept of Average

• The average (also known as the mean) is a central value in a set of numbers. It is calculated by dividing the sum of all values by the total number of values.

• Formula: Average = (Sum of all observations) / (Number of observations).

Step-by-Step Calculation

Initial Scenario: Students Only

• Number of students = 29

• Average age of students = 14 years

• Using the average formula, the total age of 29 students = Number of students 7 Average age = 29 7 14 = 406 years.

Scenario with Teacher Included

• When the teacher's age is included, the total number of people becomes 29 (students) + 1 (teacher) = 30.

• The average age increases by 1, so the new average age = Initial average + 1 = 14 + 1 = 15 years.

• Now, the total age of 30 people (29 students + 1 teacher) = Number of people 7 New average age = 30 7 15 = 450 years.

Determining the Teacher's Age

• The age of the teacher is the difference between the total age of 30 people and the total age of 29 students.

• Teacher's Age = (Total age of 30 people) - (Total age of 29 students)

• Teacher's Age = 450 - 406 = 44 years.

Alternative Approach / Shortcut Method

• This type of problem can often be solved quickly using a different approach suitable for competitive exams.

• The average age of 29 students is 14.

• When the teacher joins, the average for 30 people becomes 15. This means each of the original 29 students' age effectively increased by 1 year (from 14 to 15) and the teacher also has to be at least the new average (15).

• The teacher's age must be the new average plus the total increase distributed among the original members.

• Teacher's Age = New Average + (Increase in average 7 Original number of members)

• Teacher's Age = 15 + (1 7 29)

• Teacher's Age = 15 + 29 = 44 years.