The Indian Railways is planning to introduce new trains on a specific route. The decision-makers are faced with several constraints regarding the number of trains (T), total passengers (P), and revenue generation (R). The route can support a maximum of 5 trains per day. Each train has a capacity of 200 passengers. The fare per passenger is set at ₹500. However, for each additional train, the average occupancy drops by 10%. The first train always runs at full capacity.

## Questions:

**What is the maximum potential revenue if all trains run at full capacity?**

A) ₹2,50,000

B) ₹5,00,000

C) ₹10,00,000

D) ₹25,00,000**If only three trains run and each train runs at the respective reduced capacity, what is the total revenue generated?**

A) ₹2,70,000

B) ₹3,00,000

C) ₹3,30,000

D) ₹3,60,000**What is the maximum number of passengers that can be transported if four trains are operating?**

A) 600

B) 720

C) 800

D) 920**At what point (number of trains) does adding another train not increase total revenue?**

A) 3 trains

B) 4 trains

C) 5 trains

D) Revenue always increases with more trains

## Answers

1.**Answer: D) ₹25,00,000**

- Explanation: Maximum capacity is 5 trains × 200 passengers/train = 1000 passengers. At ₹500/passenger, maximum potential revenue is 1000 × 500 = ₹25,00,000.

2. **Answer: C) ₹3,30,000**

- Explanation: 1st train: 100% capacity = 200 passengers. 2nd train: 90% of 200 = 180 passengers. 3rd train: 80% of 200 = 160 passengers. Total passengers = 200 + 180 + 160 = 540. Total revenue = 540 × ₹500 = ₹3,30,000.

3. **Answer: B) 720**

- Explanation: 1st train: 200 passengers. 2nd train: 90% of 200 = 180. 3rd train: 80% of 200 = 160. 4th train: 70% of 200 = 140. Total = 200 + 180 + 160 + 140 = 720 passengers.

4. **Answer: B) 4 trains**

- Explanation: With each additional train, occupancy drops by 10%, so by the 4th train, the occupancy is 70% (of 200). Adding a 5th train would reduce occupancy to 60%, not increasing total revenue significantly as the drop in occupancy outweighs the benefit of adding another train.

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