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      Question

      A bag contains (2x + y) red balls, 32 black balls, and

      (3x – y) yellow balls. The probability of drawing a red ball is 4/13, and the probability of drawing a yellow ball is 1/13. Find the value of (x + y).
      A 14 Correct Answer Incorrect Answer
      B 18 Correct Answer Incorrect Answer
      C 20 Correct Answer Incorrect Answer
      D 12 Correct Answer Incorrect Answer
      E 16 Correct Answer Incorrect Answer

      Solution

      According to the question,
      {(2x + y)/(2x + y + 32 + 3x – y)} = 4/13

      Or, 26x + 13y = 20x + 128

      Or, 6x + 13y = 128…… (1)

      Also,{(3x – y)/(3x – y + 32 + 2x + y)} = 1/13
      Or, 39x – 13y = 5x + 32

      Or, 34x – 13y = 32……. (2)

      On solving equation (1) and (2), we get

      x = 4 and y = 8

      Therefore, (x + y) = 4 + 8 = 12

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