On a certain day, the ratio of the passenger in the 1 st class and the second clas travelling by train is `1 : 3`. The ratio of the fares collected from each first class and second class passenger is `30 : 1`. If the total amount collected from all the passengers is Rs 1,320. Find the amount in Rs, collected from the second class passengers.

Options

A. 240
B. 360
C. 480
D. 120

Answer

To solve the problem, we need to find the amount collected from the second class passengers given the ratios of passengers and fares. Let's break it down step by step.

### Step 1: Define the Ratios
Let the number of first class passengers be \( x \). According to the problem, the ratio of first class to second class passengers is \( 1:3 \). Therefore, the number of second class passengers will be \( 3x \).

**Hint:** Identify the variables based on the given ratios.

### Step 2: Define the Fares
Let the fare for a first class passenger be \( F \). The ratio of the fares collected from each first class to second class passenger is \( 30:1 \). Therefore, the fare for a second class passenger will be \( \frac{F}{30} \).

**Hint:** Use the given fare ratio to express the fares in terms of a single variable.

### Step 3: Calculate Total Revenue
The total amount collected from first class passengers is:
\[ \text{Total from 1st class} = x \times F \]
The total amount collected from second class passengers is:
\[ \text{Total from 2nd class} = 3x \times \frac{F}{30} = \frac{3xF}{30} = \frac{xF}{10} \]
Now, the total amount collected from all passengers is:
\[ \text{Total} = \text{Total from 1st class} + \text{Total from 2nd class} = xF + \frac{xF}{10} \]
To combine these, we can express \( xF \) as \( \frac{10xF}{10} \):
\[ \text{Total} = \frac{10xF}{10} + \frac{xF}{10} = \frac{11xF}{10} \]

**Hint:** Combine the total amounts collected from both classes to form a single equation.

### Step 4: Set Up the Equation
We know from the problem that the total amount collected is Rs 1,320. Therefore, we can set up the equation:
\[ \frac{11xF}{10} = 1320 \]

**Hint:** Use the total amount to form an equation that relates the variables.

### Step 5: Solve for \( xF \)
Multiplying both sides by 10 to eliminate the fraction gives:
\[ 11xF = 13200 \]
Now, divide both sides by 11:
\[ xF = \frac{13200}{11} = 1200 \]

**Hint:** Simplify the equation to find the product of the number of first class passengers and their fare.

### Step 6: Calculate Total from Second Class
Now, we can find the total amount collected from the second class passengers:
\[ \text{Total from 2nd class} = \frac{xF}{10} = \frac{1200}{10} = 120 \]

**Hint:** Use the value of \( xF \) to find the total collected from the second class.

### Final Answer
The amount collected from the second class passengers is Rs 120.