Multiple choice

Between two stations, the first, second and third class fares are in the ratio 9 : 7 : 2. The number of passengers travelling in a day are in the ratio 5 : 3 : 2, respectively, in the above classes. If the sale of tickets generated revenue of Rs. 98,000 that day and if 200 passengers travelled by third class, what was the fare for a first class ticket?

  1. 116

  2. 126

  3. 122

  4. 129

  5. 132
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B Correct answer
Explanation

Fares: 9x, 7x, 2x. Passengers: 5y, 3y, 2y. 2y = 200, so y = 100. Passengers are 500, 300, 200. Revenue = (500*9x) + (300*7x) + (200*2x) = 4500x + 2100x + 400x = 7000x. 7000x = 98000, so x = 14. First class fare = 9x = 9 * 14 = 126.

AI explanation

Given 200 passengers travelled by third class, the multiplier for the passenger ratio 5 : 3 : 2 is 100, meaning there are 500 first class and 300 second class passengers. The revenue ratio is calculated by multiplying fares by passengers, yielding (9 times 5) : (7 times 3) : (2 times 2), which simplifies to 45 : 21 : 4. The total ratio units are 70, so the first class total revenue is 45/70 of Rs. 98000, which equals Rs. 63000, and dividing this by 500 passengers gives a first class fare of Rs. 126.

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