Study the given information carefully and answer the given questions
The revenue of a given railway zone was collected from four primary sources— Offline Ticket Sales, Online Ticket Sales, Freight, fines during three Financial Years (FY2013-14, FY2014-15, FY2015-16)
2013-14: Total revenue collected was ₹3500 crore, Fines(₹ x crore) comprised `7 6/7%` of the total revenue and revenue from online ticket sales was ₹x+300 crore. Revenue from freight was `12%` more than that from offline ticket sales
FY 2014-15 : Revenue from online ticket sale increased by 25 crores over FY 2013-14. Revenue from offline ticket sale was 40 % of the total revenue in FY 2014-15. Revenue from Freight and Fines was in the respective ratio of `5:1`
FY 2015-16: Revenue from fines in FY 2013-14 was `11/16` th of that in FY2015-16. Revenue from online ticket sales increased by `50%` over that in FY 2014-15 and that from offline ticket sales was the average of that in FY 2013-14 and 2014- 15. Revenue from freight has been and will continue to increase steadily by ₹250 crore every financial year
If the railway profit in FY 2014-15 was `12.5%` of the total expense, what was the total expense for FY 2014- 15? (in ₹ crore)

Options

A. 2400
B. 3200
C. 3000
D. 3822

Answer

To solve the problem step by step, we will analyze the information given for each financial year and calculate the required values.

### Step 1: Calculate Fines for FY 2013-14
The total revenue for FY 2013-14 is ₹3500 crore. Fines comprised \( \frac{7 \frac{6}{7}}{100} \) of the total revenue.

\[ \text{Fines} = \frac{7 \frac{6}{7}}{100} \times 3500 = \frac{55}{7} \times 35 = 275 \text{ crore} \]

### Step 2: Calculate Online Ticket Sales for FY 2013-14
Let \( x \) be the fines, which we calculated as ₹275 crore. The revenue from online ticket sales is given as \( x + 300 \).

\[ \text{Online Ticket Sales} = 275 + 300 = 575 \text{ crore} \]

### Step 3: Calculate Offline Ticket Sales and Freight for FY 2013-14
Let \( y \) be the revenue from offline ticket sales. The revenue from freight is 12% more than that from offline ticket sales.

\[ \text{Freight} = y + 0.12y = 1.12y \]

The total revenue equation for FY 2013-14 is:

\[ y + 1.12y + 575 + 275 = 3500 \]

Combining terms:

\[ 2.12y + 850 = 3500 \]

Solving for \( y \):

\[ 2.12y = 3500 - 850 = 2650 \]
\[ y = \frac{2650}{2.12} \approx 1250 \text{ crore} \]

Now, calculate freight:

\[ \text{Freight} = 1.12 \times 1250 = 1400 \text{ crore} \]

### Step 4: Calculate Total Revenue for FY 2014-15
Revenue from online ticket sales increased by ₹25 crore over FY 2013-14:

\[ \text{Online Ticket Sales FY 2014-15} = 575 + 25 = 600 \text{ crore} \]

Revenue from offline ticket sales was 40% of total revenue in FY 2014-15. Let \( T \) be the total revenue for FY 2014-15.

\[ \text{Offline Ticket Sales} = 0.4T \]

### Step 5: Calculate Freight and Fines for FY 2014-15
The revenue from freight and fines is in the ratio of 5:1. Let the fines be \( f \) and freight be \( 5f \).

From the previous calculations, we know:

\[ \text{Fines} = 330 \text{ crore} \]
\[ \text{Freight} = 1650 \text{ crore} \]

### Step 6: Total Revenue Equation for FY 2014-15
Now we can write the total revenue equation:

\[ 0.4T + 600 + 1650 + 330 = T \]

Combining terms:

\[ 0.4T + 2580 = T \]
\[ T - 0.4T = 2580 \]
\[ 0.6T = 2580 \]
\[ T = \frac{2580}{0.6} = 4300 \text{ crore} \]

### Step 7: Calculate Total Expenses for FY 2014-15
Given that the railway profit in FY 2014-15 was 12.5% of the total expenses, let \( E \) be the total expenses.

\[ \text{Profit} = 0.125E \]

The profit can also be calculated as:

\[ \text{Profit} = \text{Total Revenue} - \text{Total Expenses} = 4300 - E \]

Setting the two equations for profit equal:

\[ 0.125E = 4300 - E \]

Rearranging gives:

\[ 1.125E = 4300 \]
\[ E = \frac{4300}{1.125} \approx 3822.22 \text{ crore} \]

### Final Answer
The total expense for FY 2014-15 is approximately ₹3822.22 crore.