The revenue of a railway zone was collected from Online Ticket Sales, Offline Ticket Sales, Freight, and Fines during three financial years: FY 2013-14, FY 2014-15, and FY 2015-16. The total revenue in FY 2013-14 was ₹3500 crore. Fines (₹X crore) made up $\frac{6}{7}$ of the total revenue, and revenue from online ticket sales was $X + 300$ crore. Revenue from freight was 12\% more than offline ticket sales.

In FY 2014-15, revenue from online ticket sales increased by ₹25 crore compared to FY 2013-14. Offline ticket sales accounted for 40\% of the total revenue in FY 2014-15. Revenue from freight and fines were in the ratio 5:1.

In FY 2015-16, revenue from fines in FY 2013-14 was $\frac{11}{16}$ of that in FY 2015-16. Online ticket sales increased by 50\% over FY 2014-15, and offline ticket sales were the average of FY 2013-14 and FY 2014-15. Freight revenue increased steadily by ₹250 crore each year.

Revenue from fines comprised two sources: vendors and passengers. The fines from passengers (₹Y crore) remained the same in FY 2013-14 and FY 2014-15. If the fine from vendors in FY 2013-14 was 55\% of that in FY 2014-15, what was the value of Y?

Question

The revenue of a railway zone was collected from Online Ticket Sales, Offline Ticket Sales, Freight, and Fines during three financial years: FY 2013-14, FY 2014-15, and FY 2015-16. The total revenue in FY 2013-14 was ₹3500 crore. Fines (₹X crore) made up $\frac{6}{7}$ of the total revenue, and revenue from online ticket sales was $X + 300$ crore. Revenue from freight was 12\% more than offline ticket sales.

In FY 2014-15, revenue from online ticket sales increased by ₹25 crore compared to FY 2013-14. Offline ticket sales accounted for 40\% of the total revenue in FY 2014-15. Revenue from freight and fines were in the ratio 5:1.

In FY 2015-16, revenue from fines in FY 2013-14 was $\frac{11}{16}$ of that in FY 2015-16. Online ticket sales increased by 50\% over FY 2014-15, and offline ticket sales were the average of FY 2013-14 and FY 2014-15. Freight revenue increased steadily by ₹250 crore each year.

Revenue from fines comprised two sources: vendors and passengers. The fines from passengers (₹Y crore) remained the same in FY 2013-14 and FY 2014-15. If the fine from vendors in FY 2013-14 was 55\% of that in FY 2014-15, what was the value of Y?

Accepted Answer

**Solution:**

1. Let the fine from vendors in FY 2014-15 be $x$ crore.

2. Then, the fine from vendors in FY 2013-14 is 55\% of $x$, which is $\frac{55}{100}x = \frac{11}{20}x$.

3. The fines consist of fines from vendors and passengers. Let the fine from passengers be $y$ crore, which remains constant in both years.

4. According to the problem:
   - Total fines in FY 2013-14 = $\frac{11}{20}x + y = 275$ crore  (Equation 1)
   - Total fines in FY 2014-15 = $x + y = 330$ crore  (Equation 2)

5. Subtract Equation 1 from Equation 2:
   $$(x + y) - \left(\frac{11}{20}x + y\right) = 330 - 275$$
   $$x - \frac{11}{20}x = 55$$
   $$\frac{20}{20}x - \frac{11}{20}x = 55$$
   $$\frac{9}{20}x = 55$$
   $$x = \frac{55 \times 20}{9} = \frac{1100}{9} \approx 122.22$$

6. Substitute $x$ back into Equation 2:
   $$122.22 + y = 330$$
   $$y = 330 - 122.22 = 207.78 \approx 208$$

**Answer:** ₹208 crore

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