The ratio of the first and second class fares between two railway stations is 4 : 1 and that of the number of passengers travelling by first and second classes is 1 : 40. If on a specific day Rs 1,100 is collected as total fare, the amount collected from the first class passengers is :

Options

A. Rs 315
B. Rs 275
C. Rs `137.50`
D. Rs100

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Understand the Ratios
We are given the following ratios:
- The ratio of first class fare to second class fare is 4:1.
- The ratio of the number of passengers traveling by first class to second class is 1:40.

### Step 2: Define Variables
Let:
- The fare for first class = 4x
- The fare for second class = x
- The number of first class passengers = y
- The number of second class passengers = 40y

### Step 3: Calculate Total Fare
The total fare collected can be expressed as:
\[ \text{Total Fare} = (\text{Number of First Class Passengers} \times \text{Fare for First Class}) + (\text{Number of Second Class Passengers} \times \text{Fare for Second Class}) \]
Substituting the variables:
\[ \text{Total Fare} = (y \times 4x) + (40y \times x) \]
This simplifies to:
\[ \text{Total Fare} = 4xy + 40xy = 44xy \]

### Step 4: Set Up the Equation
We know from the problem that the total fare collected is Rs 1,100. Therefore, we can set up the equation:
\[ 44xy = 1100 \]

### Step 5: Solve for xy
To find the value of \(xy\), we divide both sides of the equation by 44:
\[ xy = \frac{1100}{44} = 25 \]

### Step 6: Calculate the Fare Collected from First Class
The fare collected from first class passengers can be calculated as:
\[ \text{Fare from First Class} = \text{Number of First Class Passengers} \times \text{Fare for First Class} = y \times 4x \]
Since we know \(xy = 25\), we can express \(y\) in terms of \(x\):
\[ y = \frac{25}{x} \]
Substituting this back into the fare equation:
\[ \text{Fare from First Class} = \left(\frac{25}{x}\right) \times 4x = 100 \]

### Conclusion
The amount collected from the first class passengers is Rs 100.