Question

In a club, three-tenth of its members play cards only and four-tenth play carom-board only. If $30$ members play none of these games and $120$ play both; find using a Venn-diagram, the total number of members in the club.

Answer 1

Let the total number be $x$

Then according to the question, we have

$x-(\frac{3x}{10}+\frac{4x}{10})=30+120$

$\Rightarrow x-\frac{7x}{10}=150$

$\Rightarrow \frac{3x}{10}=150$

$\Rightarrow x=\frac{1500}{3}=500$