NIMCET 2020 — Mathematics PYQ

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Question

NIMCET 2020 — Mathematics PYQ

NIMCET | Mathematics | 2020

In a class of 50 students, it was found that 30 students read "Hitavad", 35 students read "Hindustan" and 10 read neither.How many students read both "Hitavad" and "Hindustan" newpapers?

Choose the correct answer:

Explanation

1. Let the sets be defined as:

$n(U) = 50$ (Total number of students)
$n(A) = 30$ (Students who read "Hitavad")
$n(B) = 35$ (Students who read "Hindustan")
$n(\text{neither}) = 10$ (Students who read neither)

2. Find the number of students who read at least one newspaper $n(A \cup B)$ :

n(A \cup B) = n(U) - n(\text{neither})

n(A \cup B) = 50 - 10

n(A \cup B) = 40

3. Use the Principle of Inclusion-Exclusion formula:

n(A \cup B) = n(A) + n(B) - n(A \cap B)

4. Substitute the known values to find $n(A \cap B)$ (both):

40 = 30 + 35 - n(A \cap B)

40 = 65 - n(A \cap B)

n(A \cap B) = 65 - 40

n(A \cap B) = 25

Final Answer:

The number of students who read both newspapers is:

25