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    Ansh and Ravi can complete a work in 24 days and 40 days respectively. They started the work, and after 8 days, Shubham joined them, who can complete
    Question

    Ansh and Ravi can complete a work in 24 days and 40 days respectively. They started the work, and after 8 days, Shubham joined them, who can complete the same work alone in 20 days. How many days will they take to complete the entire work?

    A.

    15 days

    B.

    12 days

    C.

    16 days

    D.

    20 days

    Correct option is B

    Given:

    Ansh can complete the work in 24 days.

    Ravi can complete the work in 40 days.

    Shubham can complete the work in 20 days.

    Ansh and Ravi work together for 8 days before Shubham joins.

    Concept Used:

    The rate of work is the reciprocal of time taken

    Solution:

    Rate of Ansh and Ravi = 124+140\frac{1}{24} + \frac{1}{40}​​

    =5120+3120= \frac{5}{120} + \frac{3}{120}​​

    =8120=115= \frac{8}{120} = \frac{1}{15}​​

    Work done in 8 days = 8×115=8158 \times \frac{1}{15} = \frac{8}{15}​​

    Remaining work = 18151 - \frac{8}{15}​​

    =1515815=715= \frac{15}{15} - \frac{8}{15} = \frac{7}{15}​​

    Rate of Ansh, Ravi, and Shubham = 124+140+120\frac{1}{24} + \frac{1}{40} + \frac{1}{20}​​

    =5120+3120+6120= \frac{5}{120} + \frac{3}{120} + \frac{6}{120}​​

    =760 = \frac{7}{60}​​

    Time taken by Ansh, Ravi, and Shubham to finish the remaining work:

    Time taken= 715760\frac{\frac{7}{15}}{\frac{7}{60}}​​

    =715×607=4 days= \frac{7}{15} \times \frac{60}{7} = 4 \text{ days}​​

    Total time to complete the work:

    Total time = 8 days + 4 days = 12 days 

    Alternate Solution: 

    Total work = LCM of 24, 40, 20 = 120 

    Work rate of Ansh = 12024=5\frac{120}{24} = 5 

    Work rate of Ravi = 12040=3\frac{120}{40} = 3 

    Work rate of Shubham = 12020=6\frac{120}{20} = 6 

    8 days work of Ansh and Ravi together;

    8×(5+3)=648 \times (5+3) = 64 

    Remaining work = 120 - 64 = 56 

    Time taken by Ansh, Ravi, and Shubham to finish the remaining work:

    565+3+6=4 days\frac{56}{5+3+6} = 4 \ days 

    Total time = 8 days + 4 days = 12 days 

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