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    A And B can complete a task in 60 days and 40 days respectively. If C, who can complete the same task alone in 30 days, joins A & B working togeth
    Question

    A And B can complete a task in 60 days and 40 days respectively. If C, who can complete the same task alone in 30 days, joins A & B working together 3 days after than C joins  them the number of days taken to complete remaining  task will be:

    A.

    112311 \frac{2}{3}​​

    B.

    11

    C.

    111311 \frac{1}{3}​​

    D.

    114311 \frac{4}{3}​​

    Correct option is A

    Given: 

    A can complete the work  = 60 days

    B can complete  work = 40 days 

    C can complete the work = 30 days 

    Solution:

    Total work = LCM of (60, 40,30) = 120 unit 

    Efficiency of A = 12060=2 unit/day\frac{120}{60} = 2 \ unit/day    

    Efficiency of B = 12040=3\frac{120}{40 } = 3 unit/day

    Efficiency of C = 12030\frac{120}{30}  = 4 unit/day

    3 days A and B did = (2+3) x 3 = 15 unit of work
    Now C also joins.
    All one day work now = 2+3+4 = 9 unit
    Remaining work = 120-15 = 105 unit
    they will do in =  1059\frac{105}{9}​​
                          = 353day\frac{35}{3} day​s .
    112311\frac{ 2}{3}​ days taken to complete the task

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