How many days would the 25 chalks last?

Question

Your teacher has a total of 25 chalks. When a chalk reduces to 1/5 of its original size, it gets too small for her to hold for writing and hence she keeps it aside. But your teacher hates wasting things and so, when she realizes that she has enough of these small pieces to join and make another chalk of the same size, she joins them and uses the new chalkstick. If she uses one chalk each day,

How many days would the 25 chalks last?

Answer 1

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).