Multiple choice

State the correct relationship between Quantity I and Quantity II. Quantity I. Railway fares of 1st, 2nd and 3rd classes between two stations were in the ratio of 15 : 8 : 12. The fares of 1st and 2nd class were subsequently reduced by 1/3 and 1/4, respectively. If during a day, the ratio between the passengers of 1st, 2nd and 3rd classes was 3: 7: 9 and total amount collected by the sale of tickets was Rs.303600, then find the collection from the passengers of 1st class. Quantity II. Ratio of earnings of Ashish and Aman is 7:4. If earning of Ashish increases by 25% and the earnings of the Aman decreases by 12.5%, then the ratio of Aman and Ashish earning becomes 5:2 respectively. What is Ashish earning?

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
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E Correct answer
Explanation

Quantity I: Let original fares be 15x, 8x, 12x. After reduction, fares are 10x (1st reduced by 1/3) and 6x (2nd reduced by 1/4). With passenger ratio 3:7:9, let passengers be 3k, 7k, 9k. Total = 3k(10x) + 7k(6x) + 9k(12x) = 30kx + 42kx + 108kx = 180kx = 303600. First class collection = 30kx = 30/180 × 303600 = 50600. Quantity II: Let Ashish and Aman earn 7y and 4y. After changes, Ashish earns 8.75y, Aman earns 3.5y. New ratio Aman:Ashish = 3.5y:8.75y = 14:35 = 2:5, which matches given 5:2. Ashish's earning cannot be uniquely determined - any value of y satisfies the ratio.

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