Question

The average age of boys in class is 16 years and that of the girls is 15 years. The average age for the whole class when there are equal number of girls and boys is
$\begin{align}
  & \text{a) 15 years} \\
 & \text{b) 15}\text{.5 years} \\
 & \text{c) 16 years} \\
 & \text{d) cannot be computed} \\
\end{align}$

Answer 1

Hint: Now we know that the formula to find average is $\dfrac{\text{sum of values}}{\text{number of values}}$ . Let us assume there are n number of boys and n number of girls. Hence using the formula we can find an equation for the sum of ages of boys and girls with respect to n. Now the total number of children will be the number of boys + number of girls. The sum of ages will be the sum of age of boys + sum of age of girls. Hence we can easily find the average age of class.

Complete step by step answer:
Now let us say there are n number of boys and n number of girls in class.
Now we know that the average of values is nothing but $\dfrac{\text{sum of values}}{\text{number of values}}$ .
Now we are given that the average age of buys is 16 years.
This means $\dfrac{\text{sum of ages of boys}}{\text{number of boys}}=16$
Now we have assumed the total number of boys to be n. Hence we have
$\dfrac{\text{sum of ages of boys }}{n}=16$
Hence the sum of ages of boys is 16n. ………………. (1)
Now we are also given that the average age of girls is 15 years. Hence again using the formula for average which is $\dfrac{\text{sum of values}}{\text{number of values}}$ we get.
$\dfrac{\text{sum of ages of girls}}{\text{number of girls}}=15$
Now we have assumed the total number of boys to be n. Hence we have
$\dfrac{\text{sum of age of girls}}{n}=15$
Hence the sum of ages of girls is 15n. ………………………… (2)
Now let us calculate the sum of ages of all children in a class.
Now sum of ages of all children in class = sum of ages of all boys + sum of ages of all girls.
Hence sum of ages of all children = 15n + 16n.
Now there are n boys and n girls. Hence there are 2n children in class.
Hence we get the average age in class is $\dfrac{15n+16n}{2n}$
Hence the average age is $\dfrac{31}{2}=15.5$
Hence the average age is 15.5 years.

So, the correct answer is “Option B”.

Note: Now note that when we say average age is 15.5 years it does not mean that the average age is 5 years 5 months since 0.5 years = 6 months. Also note that here we need not know the number of girls or boys to calculate as the term n gets cancelled out.