Question

In a survey, it was found that 30% of the movie-goers watch thrillers, 40% watch comedies, and 30% watch romances. It was also recorded that 10% watch only thrillers, 20% watch only comedies, while 10% watch only romances. If 15% of the movie-goers watch both thrillers and romances, find the percentage of movie-goers who watch all three genres of movies.

• A. 10%
• B. 15%
• C. 5%
• D. 20%

Answer 1

The correct option is A 10%

Using a Venn diagram to represent the given information, we find:


In the diagram, we have:

$A=Peoplewhowatchthrillersandcomediesbutnotromances$

$B=Peoplewhowatchthrillersandromancesbutnotcomedies$

$C=Peoplewhowatchromancesandcomediesbutnotthrillers$

$X=Peoplewhowatchallthreegenresofmovies$

Now, we know that:

$30\%ofthepeoplelovethrillers⟹10\%+A+X+B=30\%⟹A+X+B=20\%....\left(Eqn1\right)$

$40\%ofthepeoplelovecomedies⟹20\%+A+X+C=40\%⟹A+X+C=20\%....\left(Eqn2\right)$

$30\%ofthepeopleloveromances⟹10\%+B+X+C=30\%⟹B+X+C=20\%....\left(Eqn3\right)$

Now, we also know that 15% of the people watch both thrillers and romances.

$⟹B+X=15\%....\left(Eqn4\right)$

Combining equations 3 and 4, we get:

$B+X+C=20\%....\left(Eqn3\right)B+X=15\%....\left(Eqn4\right)⟹15\%+C=20\%⟹C=5\%$

So, we can rewrite equation 2 as:

$A+X+C=20\%....\left(Eqn2\right)⟹A+X+5\%=20\%⟹A+X=15\%$

Now, rewriting equation 1, we get:

$A+X+B=20\%....\left(Eqn1\right)⟹15\%+B=20\%⟹B=5\%$

Hence,

$C=5\%andB=5\%$

Now, including this information in equation 3, we get:

$B+X+C=20\%....\left(Eqn3\right)⟹5\%+X+5\%=20\%⟹X+10\%=20\%⟹X=10\%$

Hence, 10% of movie-goers watch all three genres of movies.