Directions: Read the following information carefully and answer the questions that follow: A train journey from P to D by an X-express has 4 classes of fares | Class | Fare | Berths per bogie | Train Composition | | :--- | :--- | :--- | :--- | | 3 tier | ₹ 300 | 72 berths per bogie | Train has 8 bogies | | AC-3 tier | ₹ 898 | 64 berths per bogie | Train has 2 bogies | | AC-2 tier | ₹ 1388 | 45 berths per bogie | Train has 2 bogies | | AC-first class | ₹ 2691 | 26 berths per bogie | Train has 1 bogie | The distance between P and D is 1100 km. Assume that the train does not stop at any station unless otherwise indicated. The running cost per kilometre: AC - bogie – ₹ 25, non-AC-bogie – ₹ 10 What is the approximate profit for the railways if the X-expressway runs at full occupancy on a particular day?

### Concept & Profit Calculation Profit is calculated by subtracting the total running cost from the total revenue generated by all bogies. $$Profit = Total Revenue - Total Cost$$ ### Step-by-Step Solution * **Total Revenue Calculation:** * 3 tier: $8 \text{ bogies} \times 72 \text{ berths} \times 300 = ₹ 1,72,800$ * AC-3 tier: $2 \text{ bogies} \times 64 \text{ berths} \times 898 = ₹ 1,14,944$ * AC-2 tier: $2 \text{ bogies} \times 45 \text{ berths} \times 1388 = ₹ 1,24,920$ * AC-first class: $1 \text{ bogie} \times 26 \text{ berths} \times 2691 = ₹ 69,966$ * Total Revenue = $1,72,800 + 1,14,944 + 1,24,920 + 69,966 = ₹ 4,82,630$ * **Total Cost Calculation (for 1100 km):** * Cost for non-AC (3 tier): $8 \text{ bogies} \times 10 \times 1100 = ₹ 88,000$ * Cost for AC bogies (5 bogies total): $5 \text{ bogies} \times 25 \times 1100 = ₹ 1,37,500$ * Total Cost = $88,000 + 1,37,500 = ₹ 2,25,500$ * **Total Profit:** * $4,82,630 - 2,25,500 = ₹ 2,57,130$ ### Exam Strategy & Shortcut By using approximations, round the revenue totals to $1.73L + 1.15L + 1.25L + 0.70L = 4.83L$. Total costs are $0.88L + 1.38L = 2.26L$. Profit is $4.83L - 2.26L = 2.57L$. The closest approximate option is ₹ 2,50,000. ### Common Pitfall A common mistake is forgetting to multiply the per-kilometer cost by both the distance (1100 km) and the number of bogies. ### Final Answer Therefore, the correct answer is **₹ 2,50,000**.