Between two railway station the ratio of fare of `1^(st)` and `2^(nd)` class was 10:7 and later on the fare is increased in the ratio 3 : 4 and 5: 9 respectively. If the ratio of no. of passengers of both tier is 3 : 5 and total fare is Rs 30900 then find the total fare of `2^(nd)` tier.

Options

A. Rs 18900
B. Rs 19400
C. Rs 20200
D. Rs 17300

Answer

To solve the problem step by step, we will follow the information provided in the question regarding the fares, the increase in fares, the ratio of passengers, and the total fare collected.

### Step 1: Define the initial fares
Let the initial fare of the 1st class be \( 10x \) and the 2nd class be \( 7x \) based on the ratio of 10:7.

### Step 2: Calculate the new fares after the increase
The fare for the 1st class is increased in the ratio of 3:4. Therefore, the new fare for the 1st class will be:
\[ \text{New fare of 1st class} = 10x \times \frac{4}{3} = \frac{40x}{3} \]

The fare for the 2nd class is increased in the ratio of 5:9. Therefore, the new fare for the 2nd class will be:
\[ \text{New fare of 2nd class} = 7x \times \frac{9}{5} = \frac{63x}{5} \]

### Step 3: Define the number of passengers
Let the number of passengers in the 1st class be \( 3y \) and in the 2nd class be \( 5y \) based on the ratio of 3:5.

### Step 4: Calculate the total fare collected
The total fare collected from the 1st class is:
\[ \text{Total fare from 1st class} = \text{New fare of 1st class} \times \text{Number of passengers} = \frac{40x}{3} \times 3y = 40xy \]

The total fare collected from the 2nd class is:
\[ \text{Total fare from 2nd class} = \text{New fare of 2nd class} \times \text{Number of passengers} = \frac{63x}{5} \times 5y = 63xy \]

### Step 5: Set up the equation for total fare
The total fare collected from both classes is given as Rs 30,900:
\[ 40xy + 63xy = 30900 \]
\[ 103xy = 30900 \]

### Step 6: Solve for \( xy \)
To find \( xy \):
\[ xy = \frac{30900}{103} = 300 \]

### Step 7: Calculate the total fare from the 2nd class
Now, we can find the total fare from the 2nd class:
\[ \text{Total fare from 2nd class} = 63xy = 63 \times 300 = 18900 \]

### Final Answer
The total fare of the 2nd class is Rs 18,900.

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