Question

All students of the school went on a trip and stayed in a hotel. On the first day of their trip $80\%$ went for a movie and $50\%$ went shopping, whereas $10\%$ took rest in their room. Which of the following conclusions can be drawn from this data?
$1$. $40\%$ students went for movie as well as shopping
$2$. $20\%$ of students went for only shopping.

• A. $1$ only
• B. $2$ only
• C. Both $1$ and $2$
• D. Neither $1$ or $2$

Answer 1

The correct option is A $1$ only

Student who went for shopping $=\frac{80}{100}$

Student who went for a movie $=\frac{80}{100}$
Student who went for shopping $=\frac{50}{100}$

Thus, $n\left(M\right)=\frac{80}{100}$

$n\left(S\right)=\frac{50}{100}$

Took rest $=\frac{10}{100}$

$\therefore n(M\cup S)=1-\frac{10}{100}=\frac{90}{100}$

Thus, $n(M\cap S)=n\left(A\right)+n\left(B\right)-n(A\cup B)$

$\Rightarrow$ Student who went for both $=n\left(M\right)+n\left(S\right)-n(M\cup S)$

$=\frac{80}{100}+\frac{50}{100}-\frac{90}{100}$

$=\frac{40}{100}$

$=40\%$

Student who went for only shopping,

$n\left(S\text{only}\right)=n\left(S\right)+n(M\cap S)$

$=\frac{50}{100}-\frac{40}{100}$

$=\frac{10}{100}$

$=10\%$

Hence, only statement $1$ is correct.

Thus, A is correct option.