Bob can finish a job in 40 days, if he works alone. Alex is twice as fast as Bob and thrice as fast as Cole in the same job. Suppose Alex and Bob work together on the first day, Bob and Cole work together on the second day, Cole and Alex work together on the third day, and then, they continue the work by repeating this three-day roster, with Alex and Bob working together on the fourth day, and so on. Then, the total number of days Alex would have worked when the job gets finished, is
Explanation:
Bob takes 40 days to finish the work. Alex takes is twice as fast as Bob and hence will take half the time taken by Bob i.e., 20 days. Alex is also thrice as fast as Cole, hence Cole will take thrice the time taken by Alex, i.e., 60 days.
Time take by Alex = 20 days Bob = 40 days Cole = 60 days
Let the total work to be done = 120 units.
∴ Efficiency of Alex = 6 units/day Bob = 3 units/day Cole = 2 units/day
Work done/cycle = 22 units.
∴ Work done in 5 cycles = 5 × 22 = 110 units
Work left after 5 cycles (15 days) = 120 – 110 = 10 units.
On 16th day Alex and Bob will together complete 9 units of work while remaining 1 unit of work will be completed by Bob and Cole on 17th day.
∴ Alex worked for 10 days in 5 complete cycles + on 16th day i.e., total 11 days.
Hence, 11.
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