RRB Technician Grade I 20 Dec 2024 Shift 1 Paper

Concept:Use the inclusion-exclusion principle for two sets to find the number of students taking at least one juice, then subtract it from the total surveyed.Explanation:Let $n(A) = 100$ be the number of students taking apple juice.Let $n(O) = 150$ be the number of students taking orange juice.The number taking both juices is $n(A \cap O) = 75$.Total students surveyed is $n(U) = 260$.Students taking at least one juice are given by the union of both sets:$$n(A \cup O) = n(A) + n(O) - n(A \cap O)$$$$n(A \cup O) = 100 + 150 - 75 = 175$$Students taking neither juice are those outside both sets, obtained by subtracting the union from the total:$$\text{Neither} = n(U) - n(A \cup O)$$$$\text{Neither} = 260 - 175 = 85$$Thus, 85 students were taking neither apple juice nor orange juice.Answer:$85$ students, which is Option B.