The ratio of 1st and 2nd classes train fairs between two stations is 3 : 1 and that of the number of pas- sengers travelling between these stations by 1st and 2nd classes is 1 : 50. If on a particular day, X 2650 be collected from the passengers travelling between these stations, then find the amount collected from 2nd class passengers.

Options

A. X 3000
B. X 3500
C. X 2800
D. X 2500

Answer

To solve the problem step by step, we will use the given ratios of train fares and the number of passengers to find the amount collected from 2nd class passengers.

### Step 1: Understand the Ratios
We are given:
- The ratio of 1st class fare to 2nd class fare is 3:1.
- The ratio of the number of passengers traveling in 1st class to those in 2nd class is 1:50.

### Step 2: Determine the Total Ratio of Fares
Let’s denote:
- The fare for 1st class as \( F_1 = 3x \)
- The fare for 2nd class as \( F_2 = x \)

Now, we can express the total fare collected from both classes based on the number of passengers:
- Let the number of 1st class passengers be \( P_1 = y \)
- Let the number of 2nd class passengers be \( P_2 = 50y \)

### Step 3: Calculate Total Amount Collected
The total amount collected from both classes can be expressed as:
\[ \text{Total Amount} = (F_1 \cdot P_1) + (F_2 \cdot P_2) \]
Substituting the values:
\[ \text{Total Amount} = (3x \cdot y) + (x \cdot 50y) = 3xy + 50xy = 53xy \]

### Step 4: Set Up the Equation
We know that the total amount collected is Rs. 2650. Therefore, we can set up the equation:
\[ 53xy = 2650 \]

### Step 5: Solve for \( xy \)
To find \( xy \):
\[ xy = \frac{2650}{53} \]
Calculating this gives:
\[ xy = 50 \]

### Step 6: Calculate the Amount Collected from 2nd Class Passengers
Now, we need to find the amount collected from 2nd class passengers:
\[ \text{Amount from 2nd class} = F_2 \cdot P_2 = x \cdot 50y \]
Since we have \( xy = 50 \), we can substitute:
\[ \text{Amount from 2nd class} = x \cdot 50y = 50 \cdot x \]
From \( xy = 50 \), we can express \( x \) as:
\[ x = \frac{50}{y} \]
Substituting back, we find:
\[ \text{Amount from 2nd class} = 50 \cdot \frac{50}{y} = 2500 \]

### Final Answer
The amount collected from 2nd class passengers is Rs. 2500.

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