Somesh, Tarun and Nikhil can complete a work separately in 45, 60 and 75 days. They started the work together but Nikhil left 5 days after the start and Somesh left 2 days before the completion of the work. In how many days will the work be completed?
Explanation:
Let the total work be equivalent to 900 units and let Somesh, Tarun and Nikhil respectively complete a, b and c units of work per day.
∴ a = 900/45 = 20; b = 15 and c = 12
Let the work be completed in n days.
For the first five days, all three people were working. For the last two days, only Tarun was working.
Hence, for the remaining n − 5 − 2 i.e. n − 7 days in between, both Somesh and Tarun were working.
Hence, considering amount of work done in each day:
5(20 + 15 + 12) + (n − 7)(20 + 15) + 2(15) = 900
∴ 235 + 35n − 245 + 30 = 900
∴ 35n = 880 i.e. n = 25.14 days
Hence, option (a).
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