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 people in the queue is less than 300, find the maximum number of people standing ahead of Pinky.

Question

Accepted Answer

To solve this problem:

1. Let the number of people ahead of Pinky be $$ 3x $$ and the number of people behind her be $$ 5x $$. The total number of people in the queue, including Pinky, is:  
   $$
   	ext{Total} = 3x + 5x + 1 = 8x + 1
   $$

2. It is given that the total number of people in the queue is less than 300:  
   $$
   8x + 1 < 300
   $$

3. Simplify to find $$ x $$:  
   $$
   8x < 299 \implies x \leq 37
   $$

4. To maximize the number of people ahead of Pinky, take the maximum possible value of $$ x = 37 $$:  
   $$
   	ext{People ahead of Pinky} = 3x = 3 	imes 37 = 111
   $$

Thus, the maximum number of people standing ahead of Pinky is **111**.