NIMCET 2020 — Mathematics PYQ

1. Identify the given values:

• Total number of students in the class, $n(U)=50$

• Number of students who read "Hitavad", $n(A)=30$

• Number of students who read "Hindustan", $n(B)=35$

• Number of students who read neither newspaper, $n(A\cup B{)}^{\prime }=10$

2. Find the total number of students who read at least one newspaper:

The number of students who read at least one newspaper is given by subtracting the students who read neither from the total number of students:

$$n(A\cup B)=n(U)-n(A\cup B{)}^{\prime }$$

$$n(A\cup B)=50-10=40$$

3. Use the Set Theory formula to find the students who read both newspapers:

According to the principle of inclusion-exclusion:

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

Substitute the known values into the equation:

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

$$40=65-n(A\cap B)$$

Rearranging the terms to find $n(A\cap B)$:

$$n(A\cap B)=65-40$$

$$n(A\cap B)=25$$

Therefore, 25 students read both "Hitavad" and "Hindustan" newspapers.

Correct Option: A) 25