Apple Tree

$\textrm{Apple Again!!}🍎🍏$

It takes $3$ days to see $5$ apples in tree. We have now $10$ apples.

To have $40$ apples we need more $30$ ones.

Now after $3$ days we will have $5-3=2$ apples

We need $30$ ones , so required days $3×15=45$ (As $2$ apple needs $3$ days. :)

Let the number of apples in the tree after $n$ days be $N$ . Then

$N = \text{number of apples today} + \text{number of new apples in }n\text{ days} - \text{number of apples I pick in }n \text{ days}$

Therefore,

$\begin{aligned} N & = 10 + \frac 53 n - n = 10 + \frac 23n \\ \implies 40 & = 10 + \frac 23 n \\ \frac 23 n & = 30 \\ \implies n & = \frac {3 \times 30}2 = \boxed {45} \ \rm days \end{aligned}$

Firstly, if I pick an apple every day, that means that I pick 3 apples every 3 days.

If my apple tree grows 5 new apples every 3 days and I pick 3 apples every 3 days, there will be 2 more apples on the tree every 3 days. We're calculating how many days before it has 40 apples, so:

10 + 2x = 40 (Where x is 3 days)

x = 15

Therefore the number of days is 15 x 3 = 45