Question

In a certain school, \[20%\] of students are below 8 years of age. The number of students above 8 years of age is \[2/3~\] of the number of students of 8 years age which is 48. What is the total number of students in the school?
A.72
B.80
C.100
D.150

Answer 1

Hint: We will first assume the total number students to be any variable. Then we will find the number of students above or equal to 8 years in terms of the variable and then one equation will be formed including that variable and after solving the equation, we will get the value of the variable which actually will give us the total number of students.

Complete step-by-step answer:
Let the number of students be $x$.
It is given that \[20%\] of students are below 8 years of age.
This also means that \[80%\] of student are above or equal to 8 years.
Therefore, the number of students above or equal to the 8 years of age $=80%\text{ of }x$
On further simplification, we get
Therefore, the number of students above or equal to the 8 years of age $=\dfrac{8x}{10}\text{ }$ …….. $\left( 1 \right)$
It is given that the number of students above 8 years of age is equal to $2/3$ times the number of students of 8 years of age.
We know that there are 48 number of students who are 8 years old.
Therefore, number of students above 8 years of age $=\dfrac{2}{3}\times 48$
On further simplification, we get
Therefore, number of students above 8 years of age $=32$
Therefore, the number of students above 8 years of age is equal to the sum of number of students above 8 years of age and number of students of 8 years of age.
Therefore, number of students above 8 years of age $=32+48=80$ ……. $\left( 2 \right)$
Equating equation 1 and equation 2, we get
$\Rightarrow \dfrac{8x}{10}\text{ =80}$
On further simplification, we get
$\Rightarrow 8x\text{ =800}$
Dividing both sides by 8, we get
$\begin{align}
  & \Rightarrow \dfrac{8x}{8}\text{ =}\dfrac{\text{800}}{8} \\
 & \Rightarrow x=100 \\
\end{align}$
Hence, the total number of students is equal to 100.
Thus, the correct option is option C.

Note: To solve such a type of problem, we should keep in mind that we should try to assume less variables so that we will not face any problem in getting the values of the variables. Also the equation that we have obtained after simplification is a linear equation in one variable. If any non-zero term is multiplied to a variable in the equation, then we simply divide both sides by that number to get the value of the variable.