In a published civil services merit list, Rohan is ranked 14^{\text{th}} from the top, whi… — State PSC Exam

In a published civil services merit list, Rohan is ranked $14^{\text{th}}$ from the top, while Seema is ranked $33^{\text{rd}}$ from the bottom. After a re-evaluation of marks, Rohan and Seema interchange their positions, resulting in Rohan becoming $48^{\text{th}}$ from the top. A third candidate, Amit, holds a rank exactly halfway between Rohan's new position and Seema's new position. If $6$ candidates ranked above Amit withdraw their candidature and $4$ new candidates are placed below Amit in the updated list, what is Amit's final rank from the bottom of the modified merit list?

Cevap: 54

Cevap

Amit's final rank from the bottom of the modified merit list is 54.

Seema's dual information (

48^{\text{th}}

from top and

33^{\text{rd}}

from bottom) gives an initial total of 80 candidates. Amit's midpoint position between

14^{\text{th}}

and

48^{\text{th}}

31^{\text{st}}

from top, placing 49 candidates below him. Accounting for 6 withdrawals above and 4 additions below leaves 53 candidates below Amit, establishing his final rank as

54^{\text{th}}

from the bottom.

Adım Adım Çözüm

Find total candidates in the original merit list using the interchange data.

Total candidates N = 80

When Rohan and Seema interchange positions, Rohan occupies Seema's original spot (

48^{\text{th}}

from top). Since Seema was

33^{\text{rd}}

from bottom,

N = 48 + 33 - 1 = 80

Calculate Amit's initial rank from the top.

Amit's initial top rank = 31st

Amit is positioned halfway between Seema's new position (

14^{\text{th}}

from top) and Rohan's new position (

48^{\text{th}}

from top), so rank =

(14 + 48) / 2 = 31^{\text{st}}

Find initial counts of candidates ranked above and below Amit.

30 candidates above, 49 candidates below

With a top rank of

31^{\text{st}}

out of 80, there are

31 - 1 = 30

candidates above Amit and

80 - 31 = 49

candidates below Amit.

Adjust counts based on candidate withdrawals and additions.

24 candidates above, 53 candidates below

Subtract 6 from candidates above (

30 - 6 = 24

) and add 4 to candidates below (

49 + 4 = 53

Calculate Amit's revised rank from the bottom.

54th from the bottom

The rank from the bottom equals (candidates below + 1), which gives

53 + 1 = 54

Anahtar Kavram

Dual Rank Position Interchange, Midpoint Computation, and Dynamic List Adjustment

Tahmini Süre:2m 30s

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