Question

In a survey of $400$ students in a school, $100$ were listed as taking apple juice, $150$ as taking orange juice and $75$ were listed as taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice?

• A. $225$
• B. $220$
• C. $250$
• D. $300$

Answer 1

Answer: (A)

$225$

Answer 2

Let $U$ denote the set of surveyed students and $A$ denote the set of students taking apple juice and $B$ denote the set of students taking orange juice. Then $n(U) = 400$, $n(A) = 100$, $n(B) = 150$ and $n(A \cap B) = 75$. Now, $n(A' \cap B') = n(A \cup B)'$ $= n(U) - n(A \cup B)= n(U) - n(A) - n(B) + n(A \cap B)$ $= 400- 100- 150 + 75 = 225$ Hence, $225$ students were taking neither apple juice nor orange juice.