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    Question

    A bag contains a certain number of fruits of three

    varieties: apple, orange, and banana. The total number of apples and oranges is 13, which is 5 more than the number of apples in the bag. If two fruits are drawn at random without replacement, the probability that the first fruit drawn is an apple and the second is a banana is 14/95. Find the total number of fruits in the bag.
    A 15 Correct Answer Incorrect Answer
    B 18 Correct Answer Incorrect Answer
    C 20 Correct Answer Incorrect Answer
    D 22 Correct Answer Incorrect Answer

    Solution

    Number of apple = 13 – 5 = 8 Number of orange = 5 Number of banana = x 14/95 = 8/(13 + x) * x/(12 + x) 380x = 7 * (13 + x) * (12 + x) 380x = 7 * (156 + 13x + 12x + x2) 7x2 – 205x + 1092 = 0 7x2 – 49x – 156x + 1092 = 0 7x(x – 7) – 156(x – 7) = 0 x = 7, 22.28(not possible) Required total = 13 + 7 = 20

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