Rahul ranked 16th from the top and 29th from the bottom among the candidates…
2023
Rahul ranked 16th from the top and 29th from the bottom among the candidates who passed an examination. Six boys did not participate in the examination, and five boys failed. How many boys were there in the class?
Answer: C. 55 — ConceptWhen a person has ranks from both ends of the same group, the group size equals the top rank plus the bottom rank minus one. Subtracting one avoids…
- A.
44
- B.
50
- C.
55
- D.
56
Show answer & explanation
Correct answer: C
Concept
When a person has ranks from both ends of the same group, the group size equals the top rank plus the bottom rank minus one.
Subtracting one avoids counting the ranked person twice. People outside that ranked group must then be added separately.
Application
Rahul is 16th from the top and 29th from the bottom among the boys who passed.
Number of boys who passed = 16 + 29 − 1 = 44.
Boys outside the passed group = 6 who did not participate + 5 who failed = 11.
Total boys in the class = 44 + 11 = 55.
Cross-check
Among 44 passing boys, a boy ranked 16th from the top has bottom rank 44 − 16 + 1 = 29, matching the given rank. Adding the 11 boys outside the passed group gives 55.