The average age of 30 boys in a class is 16, including the teacher it is 17. What is the teacher's age?

Question

The average age of $30$ boys in a class is $16$. If the teachers is included the average increases by $1$. What is the teacher's age?

Options:

1. $37$ yrs
2. $30$ yrs
3. $47$ yrs
4. $57$ yrs
5. None of these

As I tried to solve my answer is $47$ but my friend said that it is wrong am i making any silly mistake.

Actually what I did: First of all I set sum of age of all students equal to $S$ and noted $S/30=16$. Thus $S=480$. Then denoting teacher's age by $x$ I have $(480+x)/(30+1)=(16+1)$ whence $x=47$.

Answer 1

You have to solve for $\;x=$ the teacher's age:

$$\frac{a_1+\ldots+a_{30}+x}{31}=\frac{a_1+\ldots+a_{30}}{30}+1$$

With the given data, the above is much easier than it may look at first sight.

Answer 2

Let $N_a$ be the sum of all students age and $N_t$ be the teachers age,

Since there are 30 students, we can write it as $\frac{N_a}{30}=16$, so it gives $N_a=480$, now according to the aforementioned question $\frac{N_a+N_t}{30+1}=17\rightarrow480+N_t=527$, so the teacher's age is $47$.