The ratio of first class fare to second class fare is `3:1` No . Of tickets booked of first class to second class is in ratio `2:3` .Total fare collected was Rs .1800. Find fare collected from passengers of second class .

Options

A. A)Rs 1200
B. B)Rs 600
C. C)Rs 900
D. D)Rs 750

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the Ratios
We are given two ratios:
1. The ratio of first class fare to second class fare is \(3:1\).
2. The ratio of the number of tickets booked for first class to second class is \(2:3\).

### Step 2: Assign Variables
Let:
- The fare of the first class be \(3x\) (since the ratio is \(3:1\)).
- The fare of the second class be \(x\).

### Step 3: Calculate Total Tickets
Let:
- The number of first class tickets booked be \(2y\).
- The number of second class tickets booked be \(3y\).

### Step 4: Calculate Total Fare Collected
The total fare collected from first class passengers:
\[ \text{Fare from first class} = \text{Number of tickets} \times \text{Fare per ticket} = (2y) \times (3x) = 6xy \]

The total fare collected from second class passengers:
\[ \text{Fare from second class} = \text{Number of tickets} \times \text{Fare per ticket} = (3y) \times (x) = 3xy \]

### Step 5: Total Fare Equation
The total fare collected is the sum of the fares from both classes:
\[ \text{Total Fare} = \text{Fare from first class} + \text{Fare from second class} = 6xy + 3xy = 9xy \]
We know that the total fare collected is Rs. 1800:
\[ 9xy = 1800 \]

### Step 6: Solve for \(xy\)
To find \(xy\), we divide both sides by 9:
\[ xy = \frac{1800}{9} = 200 \]

### Step 7: Calculate Fare from Second Class
Now, we need to find the fare collected from second class passengers:
\[ \text{Fare from second class} = 3xy = 3 \times 200 = 600 \]

### Final Answer
The fare collected from passengers of second class is Rs. 600.

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