Understanding the Problem: Average Age Calculation
This problem involves calculating the sum of ages based on given average ages for different groups (students and teachers combined). We need to find the total age of all students and specifically Ramesh Sir's age, who is one of the teachers.
Calculating Total Age of Students
We are given that there are 20 students in a class, and their average age is 10 years.
To find the total age of the students, we multiply the number of students by their average age:
Total age of students = Number of students $\times$ Average age of students
Total age of students = $20 \times 10$ years
Total age of students = $200$ years.
Calculating Total Age of Students and Teachers Combined
The problem states that the average age of the 20 students together with their 5 teachers is 14 years.
The total number of people in this group is the sum of students and teachers:
Total people = Number of students + Number of teachers
Total people = $20 + 5 = 25$ people.
Now, we calculate the total combined age:
Total combined age = Total people $\times$ Combined average age
Total combined age = $25 \times 14$ years
Total combined age = $350$ years.
Calculating Total Age of Teachers
We can find the total age of the teachers by subtracting the total age of the students from the total combined age:
Total age of teachers = Total combined age - Total age of students
Total age of teachers = $350 - 200$ years
Total age of teachers = $150$ years.
Determining Ramesh Sir's Age
The problem states that Ramesh Sir's age is exactly the same as the average age of all their 5 teachers.
First, we calculate the average age of the teachers:
Average age of teachers = Total age of teachers / Number of teachers
Average age of teachers = $150 / 5$ years
Average age of teachers = $30$ years.
Since Ramesh Sir's age is equal to the average age of the teachers:
Ramesh Sir's age = $30$ years.
Finding the Sum of Ages of Students and Ramesh Sir
The question asks for the sum of the ages of all the students and Ramesh Sir.
Sum = Total age of students + Ramesh Sir's age
Sum = $200 + 30$ years
Sum = $230$ years.
Final Answer
The sum of the ages of all the students and Ramesh Sir is 230 years.
Important Questions from Average (Notes)
- The average age of a group of boys and girls is 18 years. If the average age of boys is 20 years and that of girls is 15 years, then what is the percentage of boys in the group?
- If the average of six consecutive even numbers is 13, then the average of the next three even numbers is:
एक परिवार में, पिता और माता की औसत आयु 35 वर्ष है । पिता, माता और उनके इकलौते बेटे की औसत आयु 27 वर्ष है । बेटे की उम्र _____________ है।
- 5 क्रमागत संख्याओं का औसत n है । यदि अगली दो संख्याएँ भी शामिल कर ली जाएँ, तो 7 संख्याओं का औसत
- एक कम्पनी में कर्मचारियों की औसत आयु 48 वर्ष है। अगले वर्ष 8 कर्मचारी सेवा से मुक्त हो जाएँगे। अगले वर्ष औसत आयु कितनी होगी ?
[सूचना : कर्मचारियों की सेवानिवृत्ति की आयु 60 वर्ष है, कम्पनी में कर्मचारियों की संख्या 30 है।]
