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    Question

    In a container, there are balls of three different

    colors: purple, silver, and gold. The sum of the number of silver and purple balls equals twice the number of gold balls. The probability of picking two silver balls is (2/45). If the total number of purple, silver, and gold balls is 30, find out the number of purple balls in the container.
    A 10 Correct Answer Incorrect Answer
    B 12 Correct Answer Incorrect Answer
    C 20 Correct Answer Incorrect Answer
    D 40 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ, Denote the number of purple, silver, and gold balls as ‘P’, ‘S’, and ‘G’ respectively. Given: P+S = 2G and P+S+G = 30. Probability for two silver balls = (2/45) implies [S(S-1)]/(30x29) = 2/45. Solving gives S(S-1) = 60, leading to S²-S-60=0, which simplifies to S = 10 (after discarding the negative solution). With S known, substitute to find G = (30 - S - P)/3 since 2G = P + S. This yields 2G = 30 - S, giving G = 10, and since P+S = 20 (from 2G = P+S), P = 10. Number of purple balls = 10.

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