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Nehal ranked 22 nd from the top and 10 th from the bottom in his class. How many students are there in his class?
33
32
30
31
31
To determine the total number of students in a single rank position, the formula used is Total = (Rank from top + Rank from bottom) - 1. Applying this, (22 + 10) - 1 equals 31.
To determine the total number of students in a single rank position, the formula used is Total = (Rank from top + Rank from bottom) - 1. Applying this, (22 + 10) - 1 equals 31.
The principle of 'Inclusion-Exclusion' is fundamental in set theory and logic, often tested in the Quantitative Aptitude and Reasoning sections of the UPSC CSAT, SSC CGL, and Banking examinations.
The rank from both ends counts the same individual twice, necessitating the subtraction of one.
Rank calculation problems frequently appear in the Logical Reasoning section of Indian competitive exams.
The formula (Top + Bottom - 1) is applicable to linear arrangements, such as queues or class rankings.
The calculation is: 32 - 1 = 31 total students.
Option A (33) is incorrect as it implies adding the ranks without adjusting for the overlapping count.
Option B (32) is incorrect as it fails to account for the double counting of the individual.
Option C (30) is incorrect as it subtracts an additional unit beyond the necessary adjustment.
D is correct тАФ The total number of students is calculated by summing the ranks from both directions and subtracting one because the student is counted twice.
This ranking concept is analogous to calendar and blood relation problems, where careful attention to 'inclusive' versus 'exclusive' counting is required to avoid off-by-one errors.
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