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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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