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    Question

    A bag contains (2x + y) red taps, 32 black taps and (3x

    – y) yellow taps. The probability of picking a red tape at random is 4/13 while the probability of picking a yellow tape at random is 1/13. Determine the value of (x + y). 
    A 10 Correct Answer Incorrect Answer
    B 17 Correct Answer Incorrect Answer
    C 12 Correct Answer Incorrect Answer
    D 24 Correct Answer Incorrect Answer
    E None of these 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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