Question

The average weight of boys in a class is 30 kg and the average weight of girls in the same class is 20 kg. If the average weight of the whole class is 23.25 kg, what could be the possible strength of boys and girls respectively in the same class?
A. 14 and 26
B. 13 and 27
C. 17 and 27
D. None of these

Answer 1

In this question we are first going to assign variables to the number of boys and girls, after that we are going to analyze the data and form equations by using the formula of calculating average which is, $Average=\dfrac{Sum\text{ }of\text{ }observations}{Number\text{ }of\text{ }observations}$. We are given the average and we have to find the number of observations but we need a sum of observations for it and for that we will use the third average equation of class and substitute it.

Complete step-by-step answer :
Let us consider the number of boys to be $x$ and the number of girls be $y$.
Now to solve the question we must first take the average of boys weight and find the sum of weight of boys in the class then take the average of girls weight and find the sum of weight of girls in the class, and at the end combine them with the average weight of the whole class equation.
So now proceeding with the question, first we will find the equation of boys average weight of whole class by using the average calculating formula, which is,
$Average\text{ }of\text{ }boys\text{ }weight=\dfrac{Sum\text{ }of\text{ }weight\text{ }of\text{ }all\text{ }boys\text{ }in\text{ }the\text{ }class}{Number\text{ }of\text{ }boys\text{ }in\text{ }the\text{ }class}$
Putting the known values in the above equation, we get,
$30=\dfrac{Sum\text{ }of\text{ }weight\text{ }of\text{ }all\text{ }boys\text{ }in\text{ }the\text{ }class}{x}$
So, the sum of weight of all boys in class is,
$Sum\text{ }of\text{ }weight\text{ }of\text{ }all\text{ }boys\text{ }in\text{ }the\text{ }class=30\times x=30x$
Now we need to find the equation of average weight of girls of whole class by using the average calculating formula, which is,
$Average\text{ }of\text{ }girls\text{ }weight=\dfrac{Sum\text{ }of\text{ }weight\text{ }of\text{ }all\text{ }girls\text{ }in\text{ }the\text{ }class}{Number\text{ }of\text{ }girls\text{ }in\text{ }the\text{ }class}$
Putting the known values in the above question, we get,
$20=\dfrac{Sum\text{ }of\text{ }weight\text{ }of\text{ }all\text{ }girls\text{ }in\text{ }the\text{ }class}{y}$
So, the sum of weight of all girls in the class is,
$Sum\text{ }of\text{ }weight\text{ }of\text{ }all\text{ }girls\text{ }in\text{ }the\text{ }class=20\times y=20y$
Now we have to put the value of these two equations in the average weight of the whole class equation and then we can find the number of girls and boys in the class. So by using the average formula for whole class, we get,
$Average\text{ }weight\text{ }of\text{ }whole\text{ }class=\dfrac{Sum\text{ }of\text{ }weight\text{ }of\text{ }all\text{ }students\text{ }in\text{ }the\text{ }class}{Number\text{ }of\text{ }students\text{ }in\text{ }the\text{ }class}$
$Average\text{ }weight\text{ }of\text{ }whole\text{ }class=\dfrac{Sum\text{ }of\text{ }weight\text{ }of\text{ }all\text{ }girls\text{ }in\text{ }the\text{ }class+Sum\text{ }of\text{ }weight\text{ }of\text{ }all\text{ }boys\text{ }in\text{ }the\text{ }class}{Number\text{ }of\text{ }girls\text{ }in\text{ }the\text{ }class+Number\text{ }of\text{ }boys\text{ }in\text{ }the\text{ }class}$
Putting the known values in the above equation, we get,
$23.25=\dfrac{20y+30x}{y+x}$
Now solving further, we get,
$23.25\left( x+y \right)=20y+30x$
$3.25y=6.75x$
$\dfrac{x}{y}=\dfrac{3.25}{6.75}$
$\dfrac{x}{y}=\dfrac{325}{675}$
$\dfrac{x}{y}=\dfrac{13}{27}$
So the number of boys $x$ is 13 and the number of girls $y$ is 27.
Hence the correct answer is,
Option B. 13 and 27

Note : If you are unable to figure out what to do in these types of questions then just put the formula you know and keep doing the question you will eventually figure out what to do in the question. Although there were two variables and one equation which is not possible to solve but in this case the constant term was 0 and the ratio of two variables matched with one of the options, so always keep an eye on options and do not get confused at the end of the solution. Sometimes you will get the question on averages which will include average speed and to solve it you will have to change the formula of $Speed=\dfrac{Distance}{Time}$ to $Average\text{ }speed=\dfrac{Total\text{ }Distance}{Total\text{ }time}=\dfrac{Total\text{ }Distance}{\dfrac{{{D}_{1}}}{{{V}_{1}}}+\dfrac{{{D}_{2}}}{{{V}_{2}}}}$ if the total journey is divided into two parts with different speed in corresponding parts, this example is for two part journey and the distance is divided by the corresponding speed with which it was covered, we can add as many parts, in the same described way, as they are asked in the question. Also we are using the formula $Time=\dfrac{Distance}{Speed}$.