The railway fares of air conditioned sleeper and ordinary sleeper class are in the ratio `4: 1`. The number of passengers travelled by air conditioned sleeper and ordinary sleeper classes were in the ratio `3 : 25`. If the total collection was Rs. 37,000, how much did air conditioner sleeper passengers pay ?

Options

A. Rs. 15,000
B. Rs. 10,000
C. Rs. 12,000
D. Rs. 16,000

Answer

To solve the problem step by step, we will follow the ratios provided and calculate the total fare paid by the air-conditioned sleeper passengers.

### Step 1: Define the Ratios
The fares of the air-conditioned sleeper and ordinary sleeper classes are in the ratio of \(4:1\).
Let:
- The fare for air-conditioned sleeper (AC) = \(4x\)
- The fare for ordinary sleeper (ORD) = \(1x\)

### Step 2: Define the Passenger Ratios
The number of passengers traveling in air-conditioned sleeper and ordinary sleeper classes are in the ratio of \(3:25\).
Let:
- Number of AC passengers = \(3y\)
- Number of ORD passengers = \(25y\)

### Step 3: Calculate Total Collection from Each Class
Now, we can calculate the total collection from each class:
- Total collection from AC passengers = \( \text{Number of AC passengers} \times \text{Fare for AC} = 3y \times 4x = 12xy \)
- Total collection from ORD passengers = \( \text{Number of ORD passengers} \times \text{Fare for ORD} = 25y \times 1x = 25xy \)

### Step 4: Calculate Total Collection
The total collection from both classes is:
\[ \text{Total Collection} = \text{Collection from AC} + \text{Collection from ORD} = 12xy + 25xy = 37xy \]

### Step 5: Set Up the Equation
We know the total collection is Rs. 37,000:
\[ 37xy = 37000 \]

### Step 6: Solve for \(xy\)
To find \(xy\), divide both sides by 37:
\[ xy = \frac{37000}{37} = 1000 \]

### Step 7: Calculate the Amount Paid by AC Passengers
Now, we need to find the amount paid by the air-conditioned sleeper passengers:
\[ \text{Amount paid by AC passengers} = 12xy = 12 \times 1000 = 12000 \]

### Conclusion
Thus, the amount paid by the air-conditioned sleeper passengers is Rs. 12,000.

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