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There were 14 students in a class. When the ages of a teacher and a new boy are added, the average age of the class increases by 10 percent while it remains the same when only the age of a boy is added. If the teacher’s age is eight more than the twice the age of new boy, then find the initial average age of the class.
  • a)
    5.53
  • b)
    13.33
  • c)
    12.53
  • d)
    14.33
  • e)
    15.43
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
There were 14 students in a class. When the ages of a teacher and a ne...
Given Information:
- Total number of students in the class = 14
- Addition of teacher's and new boy's ages increases the average age of the class by 10%
- Addition of only the new boy's age does not change the average age of the class
- Teacher's age = 2 * (new boy's age) + 8

Solution:

Let's assume:
- Initial average age of the class = A
- Sum of ages of all students and the teacher = T
- Age of the teacher = T - (14 + 1) * A
- Age of the new boy = N

Step 1: Finding the initial average age of the class
- Initially, the sum of ages of all students and the teacher = 14A + T
- When the ages of the teacher and the new boy are added, the new sum = T + (N + T - (14 + 1)A)
- According to the given information, the new average is 10% more than the initial average:
(14A + T + N + T - 15A) / 16 = 1.1A
- Simplifying the equation, we get:
2T + N = 24A ----(1)

Step 2: Finding the age of the teacher and the new boy
- Given that the teacher's age is 8 more than twice the new boy's age:
T - (14 + 1)A = 2N + 8
T = 2N + 8 + 15A ----(2)

Step 3: Substituting the value of T from equation (2) into equation (1)
- Substituting the value of T from equation (2) into equation (1), we get:
2(2N + 8 + 15A) + N = 24A
4N + 16 + 30A + N = 24A
5N + 16 = -6A
N = -6A + 16

Step 4: Finding the initial average age of the class
- Substituting the value of N back into equation (2), we get:
T = 2(-6A + 16) + 8 + 15A
T = -12A + 32 + 8 + 15A
T = 3A + 40
- Substituting the value of T back into the initial sum equation, we get:
14A + 3A + 40 = 14 * A
17A + 40 = 14A
3A = 40
A = 40 / 3 = 13.33
Therefore, the initial average age of the class is 13.33 years. Hence, option B is the correct answer.
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Community Answer
There were 14 students in a class. When the ages of a teacher and a ne...
Let the average of age of students be A and the age of new student be X. 
Age of teacher = 2X+8 
Now, as per question, (14*A + X)/15 = A, i.e. A = X
Also, (2A+8 + A + 14A)/16 = A + 10% of A = 1.1A
On solving, A = 40/3 = 13.33
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There were 14 students in a class. When the ages of a teacher and a new boy are added, the average age of the class increases by 10 percent while it remains the same when only the age of a boy is added. If the teacher’s age is eight more than the twice the age of new boy, then find the initial average age of the class.a)5.53b)13.33c)12.53d)14.33e)15.43Correct answer is option 'B'. Can you explain this answer?
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