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    Question

    Deepak and Deepti with each other can complete a work in

    60 days, Deepti and Danny in 90 days  and Deepak and Danny in 90 days. In how many days can Deepak, Deepti and Danny can complete the work if they work individually alone?
    A 120,120 and 360 days Correct Answer Incorrect Answer
    B 120,120 and 120 days Correct Answer Incorrect Answer
    C 135,125 and 310 days Correct Answer Incorrect Answer
    D 110,100 and 300 days Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ, We can say that let no of days taken by Deepak, Deepti and Danny when they work alone be taken as - x, y and z days individually. (1/x) + (1/y) = (1/60)..........eq(1) (1/y) + (1/z) = (1/90)...........eq(2) (1/x) + (1/z) = (1/90)............eq(3) While adding eq(1),(2) and (3) we get (2/x) + (2/y) + (2/z) = (1/60) + (1/90) + (1/90) = 2((1/x) + (1/y) + (1/z)) (3 + 2 + 2)/180 = (1/x) + (1/y) + (1/z) = (7/360)......eq(4) Now Subtract eq(4) with - eq 1, eq 2 and eq 3. eq(4) - (1) = (1/z) = (7/360) - (1/60) = (1/360) eq(4) - (2) = (1/x) = (7/360) - (1/90) = (1/120) eq(4) - (3) = (1/y) = (7/360) - (1/90) = (1/120) Therefore, no of days taken by Deepak, Deepti and Danny are 120,120 and 360 days individually.

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