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Zorluk: Çok zorOrder and Ranking

In a single row of students facing North, Akash is ranked 18th18^{\text{th}} from the left end, while Banya is ranked 24th24^{\text{th}} from the right end. Chetan is sitting 6th6^{\text{th}} to the right of Akash and 4th4^{\text{th}} to the left of Banya. If Akash and Banya interchange their positions while Chetan remains in his place, and then Deepa sits exactly midway between Akash's new position and Chetan's position, what is Deepa's rank from the left end of the row?

  1. 26th26^{\text{th}}Cevap
  2. B
    21st21^{\text{st}}
  3. C
    25th25^{\text{th}}
  4. D
    27th27^{\text{th}}

Cevap

The rank of Deepa from the left end of the row is 26th26^{\text{th}}.
By following the relative linear placements, Chetan's left rank is 18+6=2418 + 6 = 24, and Banya's left rank is 24+4=2824 + 4 = 28. After Akash swaps positions with Banya, Akash's new position from the left becomes 2828. Deepa sits directly midway between Chetan (24th24^{\text{th}}) and Akash's new position (28th28^{\text{th}}), which corresponds to the rank 24+282=26th\frac{24 + 28}{2} = 26^{\text{th}}.

Adım Adım Çözüm

1
Determine Chetan's position from the left end.
Since Akash is 18th18^{\text{th}} from the left and Chetan is 6th6^{\text{th}} to his right, Chetan's left-rank =18+6=24th= 18 + 6 = 24^{\text{th}}.
Moving right along a row facing North increases the positional index from the left.
2
Determine Banya's position from the left end.
Chetan is 4th4^{\text{th}} to the left of Banya, so Banya's left-rank =24+4=28th= 24 + 4 = 28^{\text{th}}.
Since Chetan is to the left of Banya, adding 44 to Chetan's position gives Banya's position from the left.
3
Find Akash's position after interchanging with Banya.
Akash takes Banya's original place, making Akash's new left-rank =28th= 28^{\text{th}}.
Interchanging positions swaps their exact ranks from the left end.
4
Calculate Deepa's position midway between Chetan's position (24th24^{\text{th}}) and Akash's new position (28th28^{\text{th}}).
Midpoint =24+282=26th= \frac{24 + 28}{2} = 26^{\text{th}} from the left end.
The exact midway index between two positions p1p_1 and p2p_2 is their arithmetic mean (p1+p2)/2(p_1 + p_2) / 2.

Anahtar Kavram

Order and Ranking involving multi-person relative placement and position interchange
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Order and Ranking

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