Multiple choice

Railway fares of 1st, 2nd and 3rd classes between two stations were in the ratio of 8 : 6 : 3. The fares of 1st and 2nd Classes were subsequently reduced by 1/6 and 1/12 respectively. If during a year, the ratio between the passengers of 1st, 2nd and 3rd classes was 9 : 12 : 26 and total amount collected by the sale of tickets was Rs 1088 Lacs, then find the collection from the passengers of 1st class?

  1. 300

  2. 320

  3. 340

  4. 360
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original fares: 8x, 6x, 3x. New fares: 1st = 8x * (5/6) = 20x/3. 2nd = 6x * (11/12) = 11x/2. 3rd = 3x. Passenger ratio: 9y, 12y, 26y. Total = (20x/3 * 9y) + (11x/2 * 12y) + (3x * 26y) = 60xy + 66xy + 78xy = 204xy = 1088. xy = 1088 / 204 = 5.33. Collection from 1st class = 60xy = 60 * 5.33 = 320.

AI explanation

Let the initial fares for 1st, 2nd, and 3rd classes be 8x, 6x, and 3x. After reductions, the new fares become 8x times 5/6, 6x times 11/12, and 3x, resulting in 20x/3, 11x/2, and 3x. The total collection is the sum of the products of passengers and new fares: 9 times 20x/3 plus 12 times 11x/2 plus 26 times 3x, which simplifies to 60x plus 66x plus 78x equaling 204x. Since 204x equals 1088 lacs, x equals 1088 divided by 204, making the 1st class collection 9 times 20x/3 equal to 320 lacs.

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