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    Question

    M, N and O can complete a task in β€˜t’, 100, and β€˜t

    + 20’ days respectively. All three started together, but after 15 days, N dropped out. Then, 30 days before the work finished, M also left. The work was finished in 60 days. Find the value of β€˜t’.
    A 13 Correct Answer Incorrect Answer
    B 25 Correct Answer Incorrect Answer
    C 20 Correct Answer Incorrect Answer
    D 10 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ,

    M worked for 30 days, N worked for 15 days and O worked for 60 days So according to question: (30/t) + (15/100) + (60/(t + 20)) = 1 β†’ (30/t) + (60/(t+20)) = 1 – (3/20) β†’ (30t + 600 + 60t)/(tΒ² + 20t) = 17/20 β†’ 17tΒ² + 340t = 600t + 12000 β†’ 17tΒ² – 260t – 12000 = 0 β†’ 17tΒ² – 340t + 80t – 12000 = 0 β†’ 17t(t – 20) + 80(t – 20) = 0 β†’ (17t + 80)(t – 20) = 0 β†’ t = 20 (valid), t = -80/17 (not valid)

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