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
In FY 2017-18, if the revenue from fines increases by `20% `over FY 2015-16, what would be the ratio between the revenues from fines and freight in FY 2017-18

Options

A. `2:3`
B. `1:5`
C. `2:5`
D. `3:4`

Answer

To solve the problem, we will go through the information step by step, calculating the revenues for each financial year and finally determining the ratio of fines to freight in FY 2017-18.

### Step 1: Calculate Revenue for FY 2013-14
- **Total Revenue**: ₹3500 crore
- **Fines**: \( \frac{7 \frac{6}{7}}{100} \) of ₹3500 crore = \( \frac{53}{7} \times 35 = ₹250 \) crore
- **Online Ticket Sales**: Let fines be \( x \) crore, then revenue from online ticket sales is \( x + 300 \) crore. Thus, \( 250 + (x + 300) + \text{Offline Ticket Sales} + \text{Freight} = 3500 \).

### Step 2: Set Up the Equation for FY 2013-14
Let the revenue from offline ticket sales be \( y \) crore and from freight be \( 1.12y \) (12% more than offline ticket sales).
- Total revenue equation:
\[ 250 + (x + 300) + y + 1.12y = 3500 \]
\[ 250 + (x + 300) + 2.12y = 3500 \]
\[ x + 2.12y = 3500 - 550 \]
\[ x + 2.12y = 2950 \]

### Step 3: Substitute Fines Value
From the previous calculation, we found \( x = 250 \).
- Substitute \( x \):
\[ 250 + 2.12y = 2950 \]
\[ 2.12y = 2950 - 250 \]
\[ 2.12y = 2700 \]
\[ y = \frac{2700}{2.12} \approx 1270.75 \text{ crore (Offline Ticket Sales)} \]
- **Freight Revenue**: \( 1.12y = 1.12 \times 1270.75 \approx 1424.84 \text{ crore} \)

### Step 4: Calculate Revenue for FY 2014-15
- **Online Ticket Sales**: Increased by ₹25 crore over FY 2013-14 = ₹575 crore.
- **Offline Ticket Sales**: 40% of total revenue.
- **Total Revenue**: \( 0.4 \times \text{Total Revenue} = y \)

Let total revenue for FY 2014-15 be \( T \):
\[ 0.4T + 0.2T + 0.2T = T \]
- Fines and Freight ratio = 5:1, thus:
\[ \text{Freight} = 5x, \text{Fines} = x \]
- Total Revenue = \( 575 + 0.4T + 5x + x = T \)

### Step 5: Calculate Revenue for FY 2015-16
- **Fines**: \( \frac{11}{16} \) of FY 2013-14 = \( \frac{11}{16} \times 250 = 173.75 \text{ crore} \)
- **Online Ticket Sales**: 50% increase over FY 2014-15 = \( 575 \times 1.5 = 862.5 \text{ crore} \)
- **Offline Ticket Sales**: Average of FY 2013-14 and FY 2014-15 = \( \frac{1270.75 + 1720}{2} \approx 1495.375 \text{ crore} \)
- **Freight**: \( 1424.84 + 250 = 1674.84 \text{ crore} \)

### Step 6: Calculate Revenues for FY 2017-18
- **Fines**: Increased by 20% over FY 2015-16 = \( 173.75 \times 1.2 = 208.5 \text{ crore} \)
- **Freight**: Increased by ₹250 crore from FY 2016-17 = \( 1674.84 + 250 = 1924.84 \text{ crore} \)

### Step 7: Calculate the Ratio of Fines to Freight in FY 2017-18
- **Fines**: ₹208.5 crore
- **Freight**: ₹1924.84 crore
- **Ratio**:
\[ \text{Ratio} = \frac{Fines}{Freight} = \frac{208.5}{1924.84} \approx 1:9.23 \]

### Final Answer
The ratio between the revenues from fines and freight in FY 2017-18 is approximately **1:9.23**.