A survey shows that 69% students like mathematics, whereas 75% like...

A survey shows that

69%

students like mathematics, whereas

75%

like chemistry. If

x%

students like both the subjects, then the maximum value of

x

Correct answer

Step-by-step solution

Let, total students in survey be $100$

If mathematics is represented by $m$ & chemistry by $c$ , then
$n\left(m \cap c\right) = x$
Given, $n\left(m\right) = 69, n\left(c\right) = 75$
Now, $n\left(m \cup c\right) = n\left(m\right) + n\left(c\right) - n\left(m \cap c\right)$
$= 69 + 75 – x$
$= 144 – x$
$∵ 75 \le n\left(m \cup c\right) \le 100$
$75 \le 144 - x \le 100$
$∴$ $44 \le x \le 69$

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