Amisha can complete a particular task in twenty days. After working for four days she fell sick for four days and resumed the work on the ninth day but with half of her original work rate. She completed the task in another twelve days with the help of a co-worker who joined her from the ninth day. The number of days required for the co-worker to complete the task alone would be ______.

Let's assume that Amisha does 10 units of work a day. So, the total work to be done is 200.

She worked for the first four days, then she worked for another 12 days.

The work done by Amisha in the first four days = 40 units

For the rest of the 12 days, she did only five units of work per day. So, the total work she did was = 40 + 12*5 = 100.

Hence, the coworker should have done 100 units in 12 days.

To finish the total work, the coworker needs = $$200\cdot\frac{12}{100}=24$$ days.