In a row, Suman is ninth from the left. Akash is eighth from the right. Nihal…
2022
In a row, Suman is ninth from the left. Akash is eighth from the right. Nihal is standing exactly at middle position between these two. What could be the minimum number of persons placed in a row?
- A.
8
- B.
9
- C.
10
- D.
12
Attempted by 40 students.
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Correct answer: C
Answer: 10 is the minimum number of persons.
Suman is 9th from the left, so Suman's position from the left = 9.
Akash is 8th from the right, so Akash's position from the left = N - 8 + 1 = N - 7 (where N is the total number of persons).
Nihal is exactly in the middle between them, so Nihal's position = (9 + (N - 7)) / 2 = (N + 2) / 2, which must be an integer.
To minimize N, place Akash to the left of Suman, which requires N - 7 < 9 ⇒ N < 16. Also Suman's 9th position means N ≥ 9. So 9 ≤ N ≤ 15 and (N + 2)/2 must be an integer, so N must be even.
The smallest even N in the range 9 to 15 is 10.
Check N = 10: Akash = 10 - 7 = 3rd from left, Suman = 9th from left, midpoint = (3 + 9) / 2 = 6. Nihal stands at position 6, exactly in the middle between Akash and Suman. Therefore the minimum number is 10.