`Answer is 31 Days`

There are 25 Chalks and teacher use 1 chalk every day, so 25 Chalks used till 1/5 of original size = 25 Days.

Teacher combines residue chalks and make 1 chalk so that she can use.

Thus, 1/5 Chalks * 25 = 5 Chalks, so to use these 5 Chalks teacher takes = 5 Days

Now she have 5 1/5 Chalks residue, so again 1 chalk created by adding 1/5 * 5 = 1 Chalk = 1 day.

Therefore, total days taken to use all the Chalks = 25 + 5 + 1 = 31 Days and teacher has 1/5 Chalk residue(which she can't use).