A, B, C can do a work in 15hr, 12hr, 20hr respectively. At 4.00 pm, they started working together and after working for 2hr, a left the work and b left 2hr before completion of the work in what time the whole work will be completed.

The amount of work completed in 2 hours is 2/15 +2/12 + 2/20 = (8 + 10 + 6) /60 = 24/60 = 2/5

There remains 3/5 of work after 2 hours.

Let the work takes 'h' hours to get completed after 2 hours of working together. And also given that 'a' went away after working 2 hours. Therefore the remaining work is done by b and c. 

Given that, b went away 2 hours before the completion of work.

Therefore, 

(h-2) / 12 + h / 20 = 3/5

(5(h-2) + 3h)/60 = 3/5

=> 8h = 46

=> h = 5.75

Therefore the whole work completed at 4 + 2 + 5+3/4  = 11:45 pm 

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Updated on: 10-Oct-2022

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