# How to get original number from a subtracted percentage number

Assume I have some values like this:

91
4550
773500
etc...


I know all of these values already subtracted with 9% like this :

100 - 9         (9      is 9% of 100)    = 91
5000 - 450      (450    is 9% of 5000)   = 4550
850000 - 76500  (76500  is 9% of 850000) = 773500


What I want?

I need a formula to give me the original value.

For instance:

I give it 91 and return me 100

or

I give it 4550 and return me 5000

Any ideas?

• If you have the original number as $x$, reducing it by nine per cent gives you $0.91x$, let's say that this is $y$. So you have $y$ and want the original value $x$? Solving the equation gives $y= 0.91x \Rightarrow x = y/0.91$. – Matti P. Aug 21 '17 at 7:20
• @MattiP. I don't have the original x value – Hamed Kamrava Aug 21 '17 at 7:30
• He knows that you do not have the original number. He is explaining how percentages work and hence how you can get back to the original number. Subtracting $9%$ is really multiplying by $.91$ so, as his formula shows, you divide by $.91$ to reverse the process. Try it with your examples. – badjohn Aug 21 '17 at 8:28
• Perhaps I should have written "Let's denote the original number by $x$" – Matti P. Aug 21 '17 at 8:57
• Yes you are right guys. Thank you all – Hamed Kamrava Aug 21 '17 at 9:24

If $x$ is the number you are looking for, and $y$ is the number you are given (the subtracted number), then you know that $$y= x - (0.09\cdot x)$$

this is an equation you should easily be able to solve for $x$ (i.e., change the equation into something like $$x=C\cdot y$$ for some constant $C$.

Hints:

• $1-\frac{9}{100} = 0.91$
• $4550 = 5000 \times 0.91$
• $5000 = 4550 \,\div\, ???$

Replace the $9$ by $x$ to be more general.

So you have $$A=B-\frac x{100} B=\left(1-\frac x{100}\right) B$$ and you know $A$ So, divide both side by the factor to get $$B=\frac{A }{1-\frac x{100} }$$

Hint, if you start with a value of $x$, subtracting $9\%$ gives you $91 \%$ of the original value (because $100 - 9 = 91$).

So the new value $y$ is given by $y = \frac{91}{100}x = 0.91x$ (or $0.91$ (a constant) times $x$).

Can you figure out how to rearrange it to get $x$ in terms of $y$?

If $y = k \times x$, where $k$ is a constant, what happens to the equation if you divide both sides by $k$?

• No I don't know how! :) – Hamed Kamrava Aug 21 '17 at 7:31
• @HamedKamrava I've edited with more hints. It's a very simple thing, but I prefer not to just give the answer away. Post if you need more help. – Deepak Aug 21 '17 at 7:36