10 workers can do a job in 12 days means that if there was only 1 worker he will do the same job in 120 days.

This implies that each worker does 1/120 th job in a day.

If 8 worker work for 5 days, they would have finished 8x5x1/120^th or 1/3^rd work

Remaining work is therefore 2/3^rd.

If half of the workers, that is 4 of them leave, the remaining workers are 4 only. In one day, they will together do 4x1/120 or 1/30^th work. Hence 2/3^rd work will be completed in 30x2/3 = 20 days.

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