Question

A survey shows $40\text{\%}$ of people like only apples, $30\text{\%}$ of people like only mangoes, if every person like atleast one fruit, then the percentage of people who like both apples and mangoes is

• A. $60\text{\%}$
• B. $30\text{\%}$
• C. $70\text{\%}$
• D. $40\text{\%}$

Answer 1

The correct option is B $30\text{\%}$

$40\text{\%}$ of people like only apples.
$30\text{\%}$ of people like only mangoes.
All of the people like some kind of fruits.
Let $A$ be the people who like apples, $B$ is the set of people who like mangoes.
$\Rightarrow n(A-B)=40;n(B-A)=30$ and $n(A\cup B)=100$
Now, using the formulae i.e.
$n(A\cup B)=n(A-B)+n(B-A)+n(A\cap B)$
$\Rightarrow n(A\cap B)=n(A\cup B)-n(A-B)-n(B-A)$
$\Rightarrow n(A\cap B)=100-40-30=30$
Hence, $30\%$ of people like both kind of fruit.