Question:medium

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

Updated On: Jan 15, 2026
Show Solution

Solution and Explanation

1. Variable Representation

Let:

  • Number of persons ahead of Pinky = \( 3x \)
  • Number of persons behind Pinky = \( 5x \)
  • \( x \) is a positive integer

The ratio of persons ahead to behind is:

\[ \frac{3x}{5x} = \frac{3}{5} \]

2. Total Persons in the Queue

Total persons = Persons ahead + Pinky + Persons behind

\[ 3x + 1 + 5x = 8x + 1 \]

Given: Total persons<300

\[ 8x + 1<300 \]

Subtract 1 from both sides:

\[ 8x<299 \]

Divide by 8:

\[ x<\frac{299}{8} \Rightarrow x<37.375 \]

The maximum possible integer value for \( x \) is 37.

3. Calculate Maximum Number of Persons Ahead of Pinky

Maximum number ahead = \( 3x \)

\[ \text{Maximum } 3x = 3 \times 37 = 111 \]

The maximum number of persons standing ahead of Pinky is 111.

Was this answer helpful?
2

Top Questions on Ratio and Proportion

Questions Asked in CAT exam

The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.
In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.
View Solution