Pinky is standing in a queue at a ticket counter. Suppose the ratio of the number of persons standing ahead of Pinky to the number of persons standing behind her in the queue is 3 : 5. If the total number of persons in the queue is less than 300, then the maximum possible number of persons standing ahead of Pinky is

Options

1. 99
2. 111
3. 100
4. none

Correct Answer

111

Explanation

Let the number of persons ahead = 3k and behind = 5k. Total people = 3k + 5k + 1 = 8k + 1 < 300 ⇒ 8k ≤ 298 ⇒ k ≤ 37.25 ⇒ k_max = 37 Maximum persons ahead = 3 × 37 = 111.

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