How much percent new content does Grandpa write in the morning? Grandpa is writing a book. Every morning he starts writing vigorously and fills a lot of pages. But post-lunch he goes through all that he's written that far (right from day one) and deletes one-fifth of it. He doesn't write anything more that day. At the end of the day the content of his book is still $20\%$ more than that at the end of the previous day. 
How much percent new content does Grandpa write in the morning?
 A: Say that after $n$ days he has $C(n)$ pages of content, and on day $n$ he writes $D(n)$ pages in the morning. Then $C(n+1)=\frac45(C(n)+D(n+1))=\frac65C(n)$. Just solve the second equation for $D(n+1)$ in terms of $C(n)$.
A: Assume the content at wakeup is $C$, and let $x>0$ be the new content written during the morning, expressed as a fraction of $C$. According to your story you have
$$C\cdot (1+x)\cdot{4\over5}\ =\ {6\over 5}\ C\ .$$
Now solve for $x$ and multiply by 100 to express this quantitiy in $\%$.
A: Hint:  you can only define it in terms of percentage increase.  Grandpa will have to write more pages each morning to keep this up.  Say he writes $x\%$ of the existing book in the morning.  How much is left after he deletes $1/5$?
A: At the end of the day he deletes one-fifth of everything. This means that he deletes one-fifth of what he had written earlier, and one-fifth of what he wrote that day. So the four-fifths of the day's work that he added should make up for the one-fifth's of the original work he deleted, and still be one-fifth more beyond that.
So four-fifths of the day's work is two-fifths of the total earlier work, which means that the day's work is half of the total earlier work.
