In a row of girls, Nayana is 15th from the left and Sumana is 23rd from the…
2022
In a row of girls, Nayana is 15th from the left and Sumana is 23rd from the right. If they interchange their positions, then Nayana becomes 18th from the left then at what position will Sumana be from the right?
- A.
25th
- B.
24th
- C.
26th
- D.
20th
Show answer & explanation
Correct answer: C
For a row of n people, a person's rank from the left (L) and rank from the right (R) at the same seat always satisfy L + R = n + 1.
When two people interchange seats, each one's new rank (from either end) equals the other person's old rank at that exact seat — the row itself does not change, only who occupies which seat.
Nayana's original rank from the left was 15th. After interchanging seats with Sumana, Nayana's new rank from the left is given as 18th. Since Nayana now sits in Sumana's original seat, this new rank equals Sumana's original rank from the left. So Sumana's original rank from the left = 18th.
Sumana's original rank from the right is given as 23rd. Applying L + R = n + 1 to Sumana's original seat: 18 + 23 = n + 1, so n = 40 girls are in the row.
After interchanging, Sumana sits in Nayana's original seat, whose rank from the left was 15th. So Sumana's new rank from the left = 15th.
Converting to a rank from the right using n = 40: R = n + 1 − L = 41 − 15 = 26th.
Check: with n = 40, Nayana's original seat (15th from the left) is also (41 − 15) = 26th from the right, and her new seat (18th from the left) is also (41 − 18) = 23rd from the right — Sumana's original rank, exactly as given. Both interchanged ranks line up, confirming Sumana's new position is 26th from the right.