In an examination, there are three subjects A, B and C. A student has to pass in each subject. 20% students failed in A, 22% students failed in B and 16% failed in C. The total number of students passing the whole examination lies between

To find the range of students who passed the whole examination, we need to determine the minimum and maximum possible number of students who failed in at least one subject.

1. To find the Minimum Pass Percentage: The maximum number of failures occurs when the failures in each subject are entirely different students (no overlap). Total maximum failures = 20 percent (A) + 22 percent (B) + 16 percent (C) = 58 percent. Minimum pass percentage = 100 percent - 58 percent = 42 percent.

2. To find the Maximum Pass Percentage: The minimum number of failures occurs when the failure groups overlap as much as possible. This happens when the smaller failure groups are subsets of the largest failure group. The largest failure group is in subject B (22 percent). If all students who failed in A and C also failed in B, the total failures would just be 22 percent. Maximum pass percentage = 100 percent - 22 percent = 78 percent.

Therefore, the total number of students passing lies between 42 percent and 78 percent. This matches Option B.