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The average age of a class of 20 students is 12 years. Out of which one student whose age is 10 year left the class and two new boys entered the class. The average of the class remains the same and the difference between the ages of new boys is 4 year. What will be the age of younger one .
  • a)
    8
  • b)
    9
  • c)
    10
  • d)
    11
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The average age of a class of 20 students is 12 years. Out of which on...
Answer – b) 9 Explanation : 240 – 10 + a+ b = 21 * 12 a+ b =22, a-b = 4. So, b= 9
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The average age of a class of 20 students is 12 years. Out of which on...
Given information:
- Total number of students in the class = 20
- Average age of the class = 12 years
- One student aged 10 years left the class
- Two new boys entered the class
- The average of the class remains the same
- Difference between the ages of new boys is 4 years

To find:
- Age of the younger one among the new boys

Solution:
Step 1: Find the sum of ages of all students before one student left the class
Sum of ages of all students = Average age of the class x Total number of students
= 12 x 20
= 240 years

Step 2: Find the sum of ages of all students after one student left the class and two new boys entered
Sum of ages of all students = Average age of the class x Total number of students
= 12 x 20
= 240 years

Since the average of the class remains the same, the sum of ages of the remaining 19 students and the two new boys is equal to the sum of ages of all 20 students before one student left the class.

Let the ages of the two new boys be x and x+4.
Then,

Sum of ages of all students after changes = (240 - 10) + x + (x+4)
= 474 + 2x

Step 3: Use the fact that the average of the class remains the same to form an equation
According to the question, the average of the class remains the same after one student left and two new boys entered. Therefore,

Average age of the class before changes = Average age of the class after changes

Sum of ages of all students before changes / Total number of students before changes = Sum of ages of all students after changes / Total number of students after changes

240 / 20 = (474 + 2x) / 21

Solving for x, we get x = 9

Therefore, the younger one among the new boys is 9 years old.

Answer: Option (B)
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The average age of a class of 20 students is 12 years. Out of which one student whose age is 10 year left the class and two new boys entered the class. The average of the class remains the same and the difference between the ages of new boys is 4 year. What will be the age of younger one .a)8b)9c)10d)11Correct answer is option 'B'. Can you explain this answer?
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