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)