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Somesh, Tarun and Nikhil can complete a work separately in 45, 60 and 75 days. They started the work together but Nikhil left after 5 days of start and Somesh left 2 days before the completion of the work. In how many days will the work be completed?
  • a)
    25 1/7
  • b)
    50 1/7
  • c)
    35 5/7
  • d)
    40 5/7
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Somesh, Tarun and Nikhil can complete a work separately in 45, 60 and ...
Let the duration in which the will be completed be 't' days
Work done by Nikhil = 1/15  ( Since He worked for 5 days)
Somesh left 2 days early that means Somesh must have worked for 't-2' days
Work done by Somesh = (t-2) * 1/45
Similarly work done by Tarun = t*1/60
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Most Upvoted Answer
Somesh, Tarun and Nikhil can complete a work separately in 45, 60 and ...
Given information:
- Somesh can complete the work in 45 days
- Tarun can complete the work in 60 days
- Nikhil can complete the work in 75 days
- Nikhil left after working for 5 days
- Somesh left 2 days before the completion of the work

Approach:
- Let's assume the total work is 300 units (LCM of 45, 60 and 75)
- Find the per day work done by each person
- Calculate the total work done by the three people in the given time frame
- Find the remaining work after Somesh left
- Calculate the time required to complete the remaining work

Calculation:
- Somesh's per day work = 300/45 = 6.67 units/day
- Tarun's per day work = 300/60 = 5 units/day
- Nikhil's per day work = 300/75 = 4 units/day
- Total work done in 5 days = (6.67+5+4) x 5 = 82.35 units
- Total work done by Somesh and Tarun in the remaining days = (6.67+5) x (x-2) = 300 - 82.35
- Solving the above equation, x = 25.14 days
- Therefore, the work will be completed in 25 1/7 days (option A)

Final Answer: The work will be completed in 25 1/7 days.
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