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    A can complete a piece of work in 20 days and B can complete the same work in 10 days. With the help of C, working together they completed the work in
    Question

    A can complete a piece of work in 20 days and B can complete the same work in 10 days. With the help of C, working together they completed the work in 5 days. The number of days in which C alone can complete the work is:

    A.

    25

    B.

    10

    C.

    15

    D.

    20

    Correct option is D

    Given:
    A can do a piece of work = 20 days
    B can do a piece of work = 10 days
    (A+B+C) can do the work in 5 days
    Concept Used :
    Let Pipe A can fill the tank in x hrs.
    Pipe A can fill a tank in 1 hrs = 1x\frac{1}{x}​​
    Solution :
    A's 1 day's work = 120 \frac{1}{20}​​
    B's 1 day's work = 110\frac{1}{10}​​
    (A+B+C)'s 1 day's work = 15\frac{1}{5}​​
    Let, C can complete the work in = x days
    C's 1 day's work =  1x\frac{1}{x}​​
    According to question,
    110+120+1x=15 =>1x=(421)20 =>1x=120 =>x=20\frac{1}{10}+\frac{1}{20} + \frac{1}{x} =\frac{1}{5} \\\ \\=>\frac{1}{x} = \frac{(4-2-1)}{20}\\\ \\=>\frac{1}{x} = \frac{1}{20}\\\ \\=> x = 20​​
    ∴ C alone can complete the work in 20 days.

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