A44
B25
C65
D54
Answer:
A. 44
Read Explanation:
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.