Question

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

Answer 1

Let's represent the number of persons standing ahead of Pinky as (3x) and the number of persons standing behind her as (5x), where (x) is a positive integer.
According to the given information, the ratio of the number of persons ahead of Pinky to the number of persons behind her is (3:5), which gives us the equation:
$[\frac{3x}{5x} = \frac{3}{5}]$
Now, let's consider the total number of persons in the queue:
Total number of persons = Persons ahead of Pinky + Pinky + Persons behind Pinky
Since the total number of persons is less than 300, we can write this as an inequality:
[3x+1+5x<300]
Simplify the inequality:
[8x+1<300]
Subtract 1 from both sides:
[8x<299]
Now, divide both sides by 8:
$[x < \frac{299}{8}]$
The maximum possible value of (x) that is less than $(\frac{299}{8})$ is (37).
Therefore, the maximum possible number of persons standing ahead of Pinky (3x) is $(3 \times 37 = 111)$.
Hence, the maximum possible number of persons standing ahead of Pinky is 111.