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 average cost of a railway ticket was rs 300 in FY 2014-15, how many passengers (approx) travelled by railways inFY2014-15? (in crore)

Options

A. `4.8`
B. `6.2`
C. `5.4`
D. `7.73`

Answer

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

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

\[ \text{Fines} = \frac{55}{7} \% \text{ of } 3500 = \frac{55}{7} \times \frac{3500}{100} = \frac{55 \times 3500}{700} = 275 \text{ crore} \]

### Step 2: Calculate the revenue from online ticket sales for FY 2013-14
The revenue from online ticket sales is given as \( x + 300 \) crore, where \( x \) is the fines calculated above.

\[ \text{Revenue from online ticket sales} = 275 + 300 = 575 \text{ crore} \]

### Step 3: Set up the equation for offline ticket sales and freight for FY 2013-14
Let the revenue from offline ticket sales be \( y \) crore. The revenue from freight is 12% more than that from offline ticket sales.

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

The total revenue can be expressed as:

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

Combining terms:

\[ 850 + 2.12y = 3500 \]

Solving for \( y \):

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

### Step 4: Calculate the revenue from freight for FY 2013-14
Using the value of \( y \):

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

### Step 5: Calculate the revenue for FY 2014-15
Revenue from online ticket sales increased by ₹25 crore over FY 2013-14:

\[ \text{Online ticket sales} = 575 + 25 = 600 \text{ crore} \]

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

\[ y = 0.4T \]

The revenue from freight and fines is in the ratio of 5:1. Let the fines be \( F \) and freight be \( 5F \):

\[ F + 5F = 6F \]

From the previous calculations, we know that freight for FY 2014-15 is:

\[ \text{Freight} = 1400 + 250 = 1650 \text{ crore} \]

Setting up the equation for total revenue:

\[ F + 1650 + 600 + y = T \]

Substituting \( y \) and \( F \):

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

Substituting \( F = \frac{1}{6} \times 1650 \):

\[ \frac{1}{6} \times 1650 + 1650 + 600 + 0.4T = T \]

Calculating \( F \):

\[ F = 330 \text{ crore} \]

Now substituting back:

\[ 330 + 1650 + 600 + 0.4T = T \]
\[ 2580 + 0.4T = T \]
\[ 0.6T = 2580 \]
\[ T = \frac{2580}{0.6} = 4300 \text{ crore} \]

### Step 6: Calculate the revenue from offline ticket sales for FY 2014-15
\[ y = 0.4 \times 4300 = 1720 \text{ crore} \]

### Step 7: Calculate total revenue from ticket sales
Total revenue from ticket sales (offline + online):

\[ \text{Total ticket revenue} = 1720 + 600 = 2320 \text{ crore} \]

### Step 8: Calculate the number of passengers
Given the average cost of a railway ticket is ₹300:

\[ \text{Number of passengers} = \frac{2320 \text{ crore}}{300} = \frac{2320}{300} \approx 7.73 \text{ crore} \]

### Final Answer
Approximately **7.73 crore** passengers traveled by railways in FY 2014-15.

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