Suman ranked 15th from the top and 28th from the bottom among the boys who…
2014
Suman ranked 15th from the top and 28th from the bottom among the boys who passed an examination in a class. Five boys abstained from the examination and eight boys failed. How many boys were there in the class?
- A.
52
- B.
54
- C.
55
- D.
56
Show answer & explanation
Correct answer: C
When a person's position is counted as r1 from one end of a line-up and r2 from the other end, the total number of people in that line-up equals r1 + r2 - 1 — the person occupying that single position is counted once from each direction, so one count must be removed to avoid double-counting them.
Among the boys who passed, Suman's rank is 15th from the top and 28th from the bottom.
Apply the position identity: total passed = 15 + 28 - 1 = 42.
The class also includes 8 boys who failed and 5 who abstained (did not appear), so total boys in the class = passed + failed + absent = 42 + 8 + 5 = 55.
Check: if 42 boys passed and Suman's rank is 28th from the bottom among them, then 42 - 28 = 14 boys rank above Suman, so Suman's rank from the top is 14 + 1 = 15th — consistent with the given data, confirming 42 passed and a class total of 55.
So the class had 55 boys.