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

Entered answer:

✅ Correct Answer: 111

As Amit Shah says, "chronology samjho":

Pinky is in a queue
The ratio of people ahead of her to people behind her is $3:5$
Total people in queue $< 300$
We need to find the maximum number of people ahead of Pinky

When we have a ratio of $3:5$ , this means for every $3$ people ahead of Pinky, there are $5$ people behind her.

We say:

Number of people ahead of Pinky $= 3x$
Number of people behind Pinky $= 5x$

Where $x$ is a positive integer (since we can't have fractional people)

We don't forget to count Pinky herself:

Total people in queue $=$ People ahead $+$ Pinky $+$ People behind

Total people in queue $= 3x + 1 + 5x = 8x + 1$

We know the total must be less than 300:

$8x + 1 < 300$

$8x < 299$

$x < \tfrac{299}{8} = 37.375$

Since $x$ must be a positive integer (we can't have 37.375 people), we take the largest integer less than 37.375.

Therefore: $x = 37$

Number of people ahead of Pinky $= 3x = 3(37) = 111$

Therefore, the maximum possible number of persons standing ahead of Pinky is 111.

When working with ratio problems involving people in queues, always remember to:

Account for the person mentioned in the problem (Pinky)
Use integer values since we can't have fractional people
Take the maximum integer value that satisfies all constraints

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