In a survey of 400 students in a school, 100 students liked apple juice, 150 students liked orange juice and 75 students liked both apple and orange juice. Find the number of students which neither liked apple nor orange juice?

In a survey of 400 students in a school, 100 students liked apple juice, 150 students liked orange juice and 75 students liked both apple and orange juice. Find the number of students which neither liked apple nor orange juice? Correct Answer 225

Calculation:

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