Smita reckoned sixteenth from the top and twenty-ninth from the bottom among those who have passed an examination. Six students did not appear in the examination and five failed in it. How many students were there in the class?

Start with the passed group. Smita is 16th from the top and 29th from the bottom among those who passed, so the passed students number 16 + 29 - 1 = 44. We subtract 1 because Smita is counted in both positions.

Now add the rest of the class. Five students failed and six did not appear, so the total is 44 + 5 + 6 = 55. Option D is correct.

• A (40): No correct use of the given figures produces 40. It misreads the failed and absent counts.
• B (44): This is only the passed group. The question asks for the whole class.
• C (50): This comes from adding only the 6 absentees to 44 and leaving out the 5 who failed.

The core concept is position-based counting: if an item is a-th from one end and b-th from the other, the total in that line is a + b - 1. It is a basic reasoning tool for UPPSC and CSAT-style questions, and the same logic helps in reading ranked merit lists for Mains answers.

Trap: adding the two positions to get 45 and forgetting to subtract Smita's own place, or treating the passed group as the entire class.