Question : The average age of 30 students in a class is 12 years. The average age of a group of 5 of the students is 10 years and that of another group of 5 of them is 14 years. The average of the remaining students is:
Option 1: 14 years
Option 2: 12 years
Option 3: 11 years
Option 4: 13 years
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Correct Answer: 12 years
Solution :
The average of 30 students = 12
$\therefore$ The sum of the ages in a class = 30 × 12 = 360
The sum of ages of the first group = 10 × 5 = 50
The sum of ages of the second group = 14 × 5 = 70
So, the sum of ages of remaining students = 360 – (70 + 50) = 240
$\therefore$ The average age of the remaining 20 students = $\frac{240}{20}$ = 12 years
Hence, the correct answer is 12 years.
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