Aspire Faculty ID #9430 · Topic: NIMCET 2020 · Just now
NIMCET 2020

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

Solution

Given: Total students = 50, read “Hitava/Hitavad” = 30, read “Hindustan” = 35, read neither = 10.

At least one: \(50 - 10 = 40\).

By inclusion–exclusion:

\(|H| + |N| - |H \cap N| = |H \cup N| = 40\)
\(30 + 35 - |H \cap N| = 40 \Rightarrow 65 - |H \cap N| = 40\)
\(|H \cap N| = 25\)

Answer: 25 students read both newspapers.

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