Question

Solve the following problems:

In class VII, $\frac{1}{5}$ of the students have taken karate as an activity, $\frac{1}{4}$ have taken athletics, $\frac{1}{3}$ have taken yoga and the remaining have taken basketball. If the number of students opting for basketball is $26$, find the total number of students in class VII.

Answer 1

Given, $\frac{1}{5}$taken karate, $\frac{1}{4}$ have taken athletics, $\frac{1}{3}$ have taken yoga and the remaining $26$ have taken basketball

Let the total number of students in class VII is $\mathrm{x}$

So, $\frac{\mathrm{x}}{5}$taken karate, $\frac{\mathrm{x}}{4}$ have taken athletics, $\frac{\mathrm{x}}{3}$ have taken yoga

According to the given condition,

$$\begin{gathered} \Rightarrow \mathrm{x}-\left(\frac{\mathrm{x}}{5}+\frac{\mathrm{x}}{4}+\frac{\mathrm{x}}{3}\right)=26 \\ \Rightarrow \mathrm{x}-\left(\frac{12\mathrm{x}+15\mathrm{x}+20\mathrm{x}}{60}\right)=26[\mathrm{LCM}\mathrm{of}5,4,3\mathrm{is}60] \\ \Rightarrow \mathrm{x}-\frac{47\mathrm{x}}{60}=26 \\ \Rightarrow \frac{60\mathrm{x}-47\mathrm{x}}{60}=26 \\ \Rightarrow 13\mathrm{x}=26\times 60 \\ \Rightarrow \mathrm{x}=\frac{26\times 60}{12} \\ \Rightarrow \mathrm{x}=2\times 60 \\ \therefore \mathrm{x}=120 \end{gathered}$$

Hence, the total number of students in the class VII is $120$.