The ratio of the first and second class train fares be tween two stations is 3 : 1 and that of the numbers of passengers travelling between the two stations by first and second classes is 1:50. If on a particular day, Rs 1,325 is collected from passengers travelling between the two stations then the amount collected from the second class passengers is :

Options

A. Rs `1,250`
B. Rs `1,000`
C. Rs 850
D. Rs 750

Answer

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

### Step 1: Understand the Ratios
The ratio of the first class train fare to the second class train fare is given as 3:1. This means for every 3 units of fare for the first class, the second class fare is 1 unit.

### Step 2: Understand the Passengers Ratio
The ratio of the number of passengers traveling in first class to those traveling in second class is given as 1:50. This means for every 1 passenger in first class, there are 50 passengers in second class.

### Step 3: Calculate the Total Fare Ratio
To find the total amount collected from both classes, we need to combine the fare and passenger ratios. We multiply the fare ratio by the number of passengers ratio:

- First Class: Fare = 3 units, Passengers = 1
- Second Class: Fare = 1 unit, Passengers = 50

Thus, the total contribution to the fare from each class can be calculated as follows:

- Total contribution from First Class = 3 (fare) * 1 (passenger) = 3 units
- Total contribution from Second Class = 1 (fare) * 50 (passengers) = 50 units

### Step 4: Combine the Contributions
Now we add the contributions from both classes to get the total ratio of amounts collected:

Total = 3 (from First Class) + 50 (from Second Class) = 53 units

### Step 5: Find the Value of One Unit
We know that the total amount collected from passengers is Rs 1,325. To find the value of one unit, we divide the total amount by the total number of units:

\[ \text{Value of 1 unit} = \frac{1325}{53} = 25 \]

### Step 6: Calculate the Amount Collected from Second Class Passengers
Now, we can calculate the amount collected from the second class passengers. Since the second class contributes 50 units, we multiply the number of units by the value of one unit:

\[ \text{Amount from Second Class} = 50 \times 25 = 1250 \]

### Final Answer
The amount collected from the second class passengers is Rs 1,250.

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