In a class of 60 students, 30 take Bengali, 20 take Hindi, 15 takes no language. How many take both Bengali and Hindi?

Question: In a class of 60 students, 30 take Bengali, 20 take Hindi, 15 takes no language. How many take both Bengali and Hindi?

Solution:
Number of students who took one or both the languages = 60 - 15 = 45

Here,
n(B) = 30
n(H) = 20
n(B∪H) = 45

Now,
n(B∩H) = n(B) + n(H) - n(B∪H)
= 30 + 20 - 45
= 5

∴ 5 students take both Bengali and Hindi.