Question

In a college, $\frac{1}{5}$ th of the student like basketball, $\frac{1}{5}$ th of the remaining students like football and $\frac{1}{8}$ th of the remaining like cricket. What is the total number of students in the college if the number of students who don't like any game is $210$

• A. $385$
• B. $275$
• C. $425$
• D. $375$
• E. None of these

Answer 1

The correct option is D $375$

Let the total no, of students in college be ${}^{\prime }{x}^{\prime }$.

no. of students who like basketball $=\frac{1}{5}\times x=\frac{x}{5}$

remaining students $=x-\frac{x}{5}=\frac{4x}{5}$

no. of students who like football $=\frac{1}{5}\times \frac{4x}{5}=\frac{4x}{25}$

remaining students = $\frac{4x}{5}-\frac{4x}{25}=\frac{4x}{5}\times \frac{4}{5}=\frac{16x}{25}$

no. of students who like cricket $=\frac{1}{8}\times \frac{16x}{25}=\frac{24}{25}$

remaining students $=\frac{16x}{25}-\frac{2x}{25}=\frac{14x}{25}$

Given ; $\frac{14x}{25}=210$

$x=\frac{210\times 25}{14}$

$\therefore$ no. of students in collage $=375$