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      Question

      In a clothing store, the ratio of shirts to trousers to

      T-shirts is 2:6:5. After Y trousers are sold, the ratio of shirts to trousers changes to 4:9. Then, after an additional 400 trousers are sold (making it Y + 400 trousers sold in total), the ratio of trousers to T-shirts becomes 1:2.
      A 1200 Correct Answer Incorrect Answer
      B 800 Correct Answer Incorrect Answer
      C 2400 Correct Answer Incorrect Answer
      D 1800 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Let the initial number of shirts, trousers and T-shirts in the store are 2n, 6n and 5n respectively.
      When Y trousers sold from the store, then remaining number of trousers = 6n - Y
      And 4: 9 = (2n): (6n - Y)
      12n - 2Y = 9n
      3n = 2Y
      n = 2Y/3
      When Y + 400 more trousers sold from the store, then remaining number of trousers = 6n - Y - (Y + 400) = 6n - 2Y - 400
      And 1: 2 = (6n - 2Y - 400): (5n)
      5n = 12n - 4Y - 800
      4Y + 800 = 7n
      4Y + 800 = 7 * 2Y/3
      2Y/3 = 800
      Y = 1200

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