Averages , Ratio and Proportion Question 9 - CAT 2022
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:
Step-by-Step Explanation
- Set up the linear sequence equation:
Let the number of people standing ahead of Pinky be 3a and the number of people standing behind her be 5a.
Including Pinky herself, the total number of people in the queue is:
Total People = 3a + 5a + 1 = 8a + 1
- Apply the upper limit constraint:
The total number of people in the queue is strictly less than 300:
8a + 1 < 300
8a < 299
a < 37.375
Since a must be an integer, the maximum possible value it can take is: a = 37
- Calculate the number of people ahead of Pinky:
Maximum people ahead = 3a = 3 × 37 = 111
Correct Answer: 111
đź’ˇ FundaMakers Tip:
Don't forget to count the person referenced in the question when setting up line or queue equations (3a + 5a + 1). Missing this +1 anchor is a common trap that leads to incorrect values.