In a class of 55, 31 students like maths and 29 like science .It is given that all the students like at least one of the two.Then, find the number of students who like both the subjects.

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Solution

The correct option is A (5)

The total number of students in the class $= 55$
Given that all the students like either of the subjects,

So the number of students who like maths or science =55
The number of students who like maths = 31
The number of students who like science = 29
Let n (A) be the number of students who like maths, n(B) be the number of students who like science, then
$n (A) + n (B) = n (A \cup B) + n (A \cap B)$
$\Rightarrow n (A \cap B) = n (A) + n (B) - n (A \cup B)$
$∴ n (A \cap B) = 31 + 29 - 55 = 5$
Hence, the number of students who like both the subjects is $5$ .

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