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      Question

      The average scores of candidates from Institute A and

      Institute B in a Mock test (out of 150 marks) are 80 and 90, respectively. The number of candidates in Institute B is 33.33% less than that in Institute A. Quantity I: If the difference in the number of candidates between both Institutes is 48, determine the number of candidates in Institute B. Quantity II: Calculate the combined average score of candidates from both Institutes. Quantity III: A candidate from Institute A scored 48% of the total marks and obtained 18 marks more than the passing score. What is the passing score? In the question, three quantities i.e. Quantity I, Quantity II and Quantity III are given. Solve the given quantities to establish the correct relation between them and choose the correct option.
      A Quantity I > Quantity II > Quantity III Correct Answer Incorrect Answer
      B Quantity I < Quantity II < Quantity III Correct Answer Incorrect Answer
      C Quantity I > Quantity II < Quantity III Correct Answer Incorrect Answer
      D Quantity I < Quantity II > Quantity III Correct Answer Incorrect Answer
      E Quantity I = Quantity II = Quantity III or relation can't be established Correct Answer Incorrect Answer

      Solution

      ATQ, Quantity I, candidates in institute A = 48 × 3 = 144 candidates in institute B = 144 × 2/3 = 96 Quantity II, candidates in institute A = 3x candidates in institute B = 2x Average marks of students of both class = (3x × 80 + 2x × 90)/(3x + 2x) = (240 + 180)/5 = 420/5 = 84 Quantity III, Passing Marks = 150 × 0.48 - 18 = 72 - 18 = 54 Hence, Quantity I > Quantity II > Quantity III

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