In a class of boys and girls, Ajay's rank is 12th and Anu's rank is 8th.…
2014
In a class of boys and girls, Ajay's rank is 12th and Anu's rank is 8th. Ajay's rank among boys is 6th and Anu's rank among girls is 3rd. In the class, Anu's rank is 52nd from the other end. From the other end, Ajay's rank among the boys is 26th. Which of the following is Anu's rank among girls from other end?
- A.
23rd
- B.
28th
- C.
26th
- D.
None of the above
Attempted by 3 students.
Show answer & explanation
Correct answer: C
Concept:
For a linear arrangement, if a person's rank is known from one end and from the other end, the count of people in that arrangement satisfies the identity: Total = (Rank from one end) + (Rank from the other end) minus 1. This identity applies equally to the whole class, or to any subgroup (such as boys or girls), as long as both end-ranks used belong to the SAME subgroup.
Applying it to this question:
Total students = Anu's rank from front (8) + Anu's rank from the other end (52) minus 1 = 59.
Total boys = Ajay's rank among boys from front (6) + Ajay's rank among boys from the other end (26) minus 1 = 31.
Total girls = Total students minus Total boys = 59 minus 31 = 28.
Anu's rank among girls from the other end = Total girls minus Anu's rank among girls from front (3) plus 1 = 28 minus 3 plus 1 = 26.
Cross-check:
Cross-check: Total boys + Total girls = 31 + 28 = 59, which matches the total students found in the first step, confirming the subgroup split is consistent. Also, applying the same identity to girls alone: Anu's front rank among girls (3) + her rank from the other end (26) minus 1 = 28, which matches the total girls found earlier.
Result:
So Anu's rank among girls from the other end is 26th.