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

Correct Answer: 111

Step 1: Let Variables Represent the Scenario

Let the number of persons ahead of Pinky be \( 3x \) Let the number of persons behind Pinky be \( 5x \) (since the ratio is \( 3:5 \))

Step 2: Total Number of Persons in the Queue

Total number of persons in the queue is: \[ 3x + 1 + 5x = 8x + 1 \] We're told: \[ 8x + 1 < 300 \]

Step 3: Solve the Inequality

Subtract 1 from both sides: \[ 8x < 299 \] Divide by 8: \[ x < \frac{299}{8} = 37.375 \Rightarrow \text{Maximum integer value of } x = 37 \]

Step 4: Calculate Persons Ahead of Pinky

Using \( x = 37 \): \[ \text{Persons ahead of Pinky} = 3x = 3 \times 37 = \boxed{111} \]

Final Answer:

\[ \boxed{\text{Maximum persons ahead of Pinky} = 111} \]

Answer 2

Step 1: Assume Representation

Let Pinky be surrounded by:

• \(3a\) people ahead of her
• \(5a\) people behind her

Total number of people in the queue (including Pinky) is: \[ 3a + 5a + 1 = 8a + 1 \]

 

Step 2: Apply the Total Constraint

Given: total people in the queue is less than 300: \[ 8a + 1 < 300 \Rightarrow 8a < 299 \Rightarrow a < 37.375 \] Since \(a\) must be a whole number, the maximum possible value of \(a\) is: \[ a = 37 \]

Step 3: Calculate People Ahead of Pinky

Using \( a = 37 \): \[ \text{People ahead of Pinky} = 3a = 3 \times 37 = \boxed{111} \]

Final Answer:

\[ \boxed{111} \] is the maximum number of people that might be standing in front of Pinky.