Question

The average age of 50 students of a class is 12 years. The average age along with their teacher is 12.5 years. What is the age of their teacher?
(a) 25.5
(b) 37.5
(c) 39.5
(d) 37

Answer 1

Hint: We know the formula for average is equal to the division of sum of all the observations to the number of observations. Now, it is given that the average age of 50 students is 12 so we are going to divide the sum of 50 students to 50 and then equate this division to 12. After that, cross multiply this equation and get the sum of the age of 50 students. Then let us suppose the age of teacher is x years then add this age of teacher in the sum of age of 50 students and divide this addition to 51 and equate it to 12.5. From this equation, we will get the value of x.

Complete step-by-step answer:
In the above problem, we have given the average age of 50 students as 12 years.
We know the formula of average as follows:
$\dfrac{\text{Sum of observations}}{\text{Total number of observations}}$
Now, substituting total number of observations as 50 and equate this division to 12 and we get,
$\dfrac{\text{Sum of observations}}{50}=12$
Let us write the sum of observations as “sum of 50 observations” in the above equation and we get,
$\dfrac{\text{Sum of 50 observations}}{50}=12$
Now, cross multiplying the above equation we get,
$\text{Sum of 50 observations}=12\times 50$
$\Rightarrow \text{Sum of 50 observations}=600$
Let us suppose the age of the teacher be x years so adding the x years in the above sum then the number of observations becomes 51 and we get the sum of 51 observations as:
$\text{Sum of 51observations}=600+x$
Now, dividing sum of 51 observations by 51 and equating this division to 12.5 we get,
$\dfrac{\text{Sum of 51 observations}}{51}=\dfrac{600+x}{51}=12.5$
Rearranging the above equation we get,
$\dfrac{600+x}{51}=12.5$
Cross multiplying the above equation we get,
$\begin{align}
  & 600+x=12.5\times 51 \\
 & \Rightarrow 600+x=637.5 \\
\end{align}$
Subtracting 600 on both the sides of the above equation we get,
$\begin{align}
  & x=637.5-600 \\
 & \Rightarrow x=37.5 \\
\end{align}$
Hence, we got the age of the teacher as 37.5 years

So, the correct answer is “Option (b)”.

Note: The mistake that could be possible in the above problem is the calculation mistake in forgetting the decimals. For e.g. the mistake that could be possible is that you might forget to write .5 after 37 and interestingly you can find one of the options in which age is given as 37 so make sure you won’t succumb to make such mistakes.