UPSC NDA Math Model Paper 6

Let X = Total number of students in class, A = Number of students who liked apple juice and O = Number of students who liked orange juice.
Given: n (X) = 400, n (A) = 100, n (O) = 150 and n (A ∩ O) = 75.
We have to find the number of students who study neither liked apple nor orange juice.
i.e n (A ∪ O)’
⇒ n (A ∪ O) = n (A) + n (O) – n (A ∩ O)
⇒ n (A ∪ O) = 100 + 150 - 75 = 175
We know that, n (A ∪ O)' = n (X) – n (A ∪ O)
⇒ n (A ∪ O)' = 400 - 175 = 225.