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.

Answer 2

Assume that Pinky is surrounded by 3a and 5a people, respectively.
A total of \(3a + 5a + 1\) (including pinky) equals 
\(8a + 1\); 
\(8a + 1 < 300; 8a < 299. \)
\(⇒ a < 37.375.\)
A can only take a maximum of 37 values.
Assuming \(3a = 3\times 37 = 111\), 
the greatest number of people that might possibly be in front of Pinky is 3.