Discussion

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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