Question

The average age of 12 students is 16 years. If one more student is included and his age is 12 years more than the average age of 13 students, then the age of 13th student is

• A. 28 years
• B. 25 years
• C. 27 years
• D. 29 years

Answer 1

The correct option is D 29 years

Let x be the age of the ${13}^{th}$ student and $S_{12}$ be the sum of the ages of 12 students.
Average of 12 students = $\frac{\text{Sum of the ages of 12 students}}{12}$
$\Rightarrow 16=\frac{S_{12}}{12}$
$\Rightarrow S_{12}=16\times 12$
Given: x =$12+\frac{S_{12}+x}{13}$
$\Rightarrow \frac{S_{12}+x}{13}=x-12$
$\Rightarrow S_{12}+x=13x–12\times 13$
$\Rightarrow 12\times 16+x=13x–12\times 13$
$\Rightarrow 12\times 16+12\times 13=13x–x$
$\Rightarrow 12(16+13)=12x$
$\Rightarrow x=29$ years
Thus, the age of ${13}^{th}$ student is 29 years.
Hence, the correct answer is option (b).