Question : The average age of 40 students in a class is 16 years. After the admission of 10 new students to the class, the average becomes 15 years. If the average age of 5 of the new students is 11 years, then the average age (in years) of the remaining 5 new students is:
Option 1: 10
Option 2: 12
Option 3: 16
Option 4: 11
Correct Answer: 11
Solution :
The average age of 40 students = 16 years
On admission of 10 new students average = 15 years
Average of 5 new students = 11
Formula used:
Average = Average = $\frac{\text{Sum of all observations}}{\text{Number of observations}}$
Calculation:
The sum of all ages of 40 students = 40 × 16 = 640 years
After the admission of 10 new students, the number of students now = 40 + 10
= 50
The sum of all ages after the admission of 10 new students = 50 × 15 = 750 years
The sum of ages of 5 new students = 5 × 11 = 55 years
Now the sum of the ages of the remaining 5 new students = Sum of all ages after the admission of 10 new students - Sum of all ages of 40 students - Sum of ages of 5 new students
= 750 - 640 - 55
= 750 - 695
= 55 years
Average of 5 new students = $\frac{55}{5}$ = 11
$\therefore$ The Average of 5 new students is 11.
Hence, the correct answer is 11.
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