Working with percentages: if 30000 is left after donating 4%, 7%, 8% to various causes, what was the original wealth?

Question

Recently in an aptitude test I came across a type of question as follows:

A cat eats 75% rats in a room, it can go in all rooms, if 1 rat remains in the fourth room, how many rats where there initially?

How are these types of questions solved?

Another one was, One rich guy donated 4% to Hospital, 7% to old age home, 8% to something, his remaining wealth was 30000$, what was his original wealth? I forgot the correct numbers and options but I'd surely like to know how to approach these questions.

Answer 1

suppose x was the rich guy's original wealth. $$x - (\frac{4}{100}x + \frac{7}{100}x + \frac{8}{100}x)= 30,000$$ $$100x - (4x + 7x + 8x)= 3,000,000$$ $$81x = 3,000,000$$ $$x = \frac{3,000,000}{81}$$

Answer 2

For the first problem we have to presume that initially all rooms have equal number of rats. 1 rat was left in the last room, so -

 75% of x = 1;
 x=4 where x = total rats in 4th room
 Total rats = 4*4 = 16 if and only there are equal number of rats in each room.

Answer 3

For the 1st question, if cat eats 75% of the rat then 25% rat she can't and they remain alive. So, $1=25\%$ of $x$ where $x$ is the number of rats in the fourth room. Or, there were 4 rats in the fourth room, and she ate 3 delicious rats.

Now, you can not calculate the count of rats of other three rooms because you don't have data for them.

Second question,

If T represents total wealth he has, and H,O,S denote his donations to hospital, oldage home and something.

Then,

$$T-(H+O+S)=30000$$ $$T-(0.04T+0.07T+0.08T)=30000$$

I think you can calculate from here :)