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The average age of students in a class is 25 years. If the oldest and the youngest students are excluded, the average is equal to 2 more than the average age of the youngest and the oldest. The oldest student is 28 years old and is 8 years older than the youngest. What is the number of students in the class?
- a)2
- b)4
- c)6
- d)8
- e)10
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The average age of students in a class is 25 years. If the oldest and...
Given:
- The average age of students in a class is 25 years.
- The oldest student is 28 years old and is 8 years older than the youngest.
- The average age, after excluding the oldest and the youngest students, is equal to 2 more than the average age of the youngest and the oldest.
To find:
Number of students in the class.
Solution:
Let's assume the number of students in the class is 'n'.
Step 1: Find the average age of the class:
The average age of the class is given as 25 years. This means that the sum of ages of all the students divided by the number of students is equal to 25.
So, the sum of ages of all the students = 25n.
Step 2: Find the age of the youngest student:
We are given that the oldest student is 28 years old and is 8 years older than the youngest.
So, let the age of the youngest student be 'y'.
Therefore, the age of the oldest student = y + 8.
Step 3: Find the sum of ages after excluding the oldest and youngest students:
The average age, after excluding the oldest and the youngest students, is equal to 2 more than the average age of the youngest and the oldest.
So, the sum of ages after excluding the oldest and the youngest students = (y + y + 8)(n - 2).
Step 4: Equate the two sums of ages:
Since the sum of ages of all the students is equal to the sum of ages after excluding the oldest and the youngest students, we can equate the two sums:
25n = (y + y + 8)(n - 2).
Step 5: Solve the equation:
Let's solve the equation to find the value of 'n'.
25n = (2y + 8)(n - 2)
25n = 2ny + 8n - 4y - 16
17n = 2ny - 4y - 16
17n = y(2n - 4) - 16
17n + 16 = y(2n - 4)
Since the average age is always a whole number, the sum of ages should also be a multiple of the number of students.
Therefore, y(2n - 4) must be a multiple of (17n + 16).
Considering the options given:
a) 2 students: 2(2n - 4) = 4n - 8 (not a multiple of 17n + 16)
b) 4 students: 4(2n - 4) = 8n - 16 (not a multiple of 17n + 16)
c) 6 students: 6(2n - 4) = 12n - 24 (not a multiple of 17n + 16)
d) 8 students: 8(2n - 4) = 16n - 32 (not a multiple of 17n + 16)
e) 10 students: 10(2n - 4) = 20n - 40 (not a multiple of 17n +
- The average age of students in a class is 25 years.
- The oldest student is 28 years old and is 8 years older than the youngest.
- The average age, after excluding the oldest and the youngest students, is equal to 2 more than the average age of the youngest and the oldest.
To find:
Number of students in the class.
Solution:
Let's assume the number of students in the class is 'n'.
Step 1: Find the average age of the class:
The average age of the class is given as 25 years. This means that the sum of ages of all the students divided by the number of students is equal to 25.
So, the sum of ages of all the students = 25n.
Step 2: Find the age of the youngest student:
We are given that the oldest student is 28 years old and is 8 years older than the youngest.
So, let the age of the youngest student be 'y'.
Therefore, the age of the oldest student = y + 8.
Step 3: Find the sum of ages after excluding the oldest and youngest students:
The average age, after excluding the oldest and the youngest students, is equal to 2 more than the average age of the youngest and the oldest.
So, the sum of ages after excluding the oldest and the youngest students = (y + y + 8)(n - 2).
Step 4: Equate the two sums of ages:
Since the sum of ages of all the students is equal to the sum of ages after excluding the oldest and the youngest students, we can equate the two sums:
25n = (y + y + 8)(n - 2).
Step 5: Solve the equation:
Let's solve the equation to find the value of 'n'.
25n = (2y + 8)(n - 2)
25n = 2ny + 8n - 4y - 16
17n = 2ny - 4y - 16
17n = y(2n - 4) - 16
17n + 16 = y(2n - 4)
Since the average age is always a whole number, the sum of ages should also be a multiple of the number of students.
Therefore, y(2n - 4) must be a multiple of (17n + 16).
Considering the options given:
a) 2 students: 2(2n - 4) = 4n - 8 (not a multiple of 17n + 16)
b) 4 students: 4(2n - 4) = 8n - 16 (not a multiple of 17n + 16)
c) 6 students: 6(2n - 4) = 12n - 24 (not a multiple of 17n + 16)
d) 8 students: 8(2n - 4) = 16n - 32 (not a multiple of 17n + 16)
e) 10 students: 10(2n - 4) = 20n - 40 (not a multiple of 17n +
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Community Answer
The average age of students in a class is 25 years. If the oldest and...
If the oldest student is 28 years old, the youngest will be 20 years old.
So, average age of the oldest and the youngest = (28 + 20)/2 = 24 years
Average of all the students together = 25
Let us assume that n students are there in the class.
∴ 26(n - 2) + 28 + 20 = 25n
∴ n = 4
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The average age of students in a class is 25 years. If the oldest and the youngest students are excluded, the average is equal to 2 more than the average age of the youngest and the oldest. The oldest student is 28 years old and is 8 years older than the youngest. What is the number of students in the class?a)2b)4c)6d)8e)10Correct answer is option 'B'. Can you explain this answer?
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The average age of students in a class is 25 years. If the oldest and the youngest students are excluded, the average is equal to 2 more than the average age of the youngest and the oldest. The oldest student is 28 years old and is 8 years older than the youngest. What is the number of students in the class?a)2b)4c)6d)8e)10Correct answer is option 'B'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about The average age of students in a class is 25 years. If the oldest and the youngest students are excluded, the average is equal to 2 more than the average age of the youngest and the oldest. The oldest student is 28 years old and is 8 years older than the youngest. What is the number of students in the class?a)2b)4c)6d)8e)10Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The average age of students in a class is 25 years. If the oldest and the youngest students are excluded, the average is equal to 2 more than the average age of the youngest and the oldest. The oldest student is 28 years old and is 8 years older than the youngest. What is the number of students in the class?a)2b)4c)6d)8e)10Correct answer is option 'B'. Can you explain this answer?.
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