Question

Out of $32$ persons, $30$ invest in national savings certificates and $17$ invest in shares. What is the number of persons who invest in both?

• A. $13$
• B. $15$
• C. $17$
• D. $19$

Answer 1

The correct option is B

$15$

Explanation for correct option

Calculating the number of persons who invest in both national savings and shares:

Let $A$ be the set of people invested in national savings certificates and $B$ be the set of people invested in shares.

Now,

Number of people invested in national savings $=n\left(A\right)$

Number of people invested in shares$=n\left(B\right)$

Number of people invested in both national savings and shares $=n(A\cap B)$

Total number of People $=n(A\cup B)$

Hence, the total number of persons invested in both national savings and shares:

$$\begin{gathered} n(A\cup B)=n\left(A\right)+n\left(B\right)–n(A\cap B) \\ \Rightarrow 32=30+17–n(A\cap B) \\ \Rightarrow n(A\cap B)=15 \end{gathered}$$

Hence, the correct answer is Option (B).