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    Question

    The work can be completed

    by 'P' boys in 16 days, and by (P + 1) girls in 20 days. Additionally, if 8 boys and 12 girls work together, they can complete the same task in 5 days. Find the value of 'P'.
    A 5 Correct Answer Incorrect Answer
    B 8 Correct Answer Incorrect Answer
    C 12 Correct Answer Incorrect Answer
    D 20 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ, Let the boys and girls can be defined as 'b' and 'g' respectively Pb*16 = (P+1)*g*20 4Pb = (5P+5)*g b/ g = (5P+5)/ 4P P*(5P+5)*16 = [8*(5P+5) + 12*4P]*5 80P² + 80P = 440P + 200 80P² - 360P – 200 = 0 2P² - 9P – 5 = 0 2P² - 10P + P – 5 = 0 2P (P - 5) + 1 (P - 5) = 0 (P - 5) (2P + 1) = 0 P = 5, -1/2 P = 5

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